The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 X 1 1 X 1 2X 1 1 1 1 1 1 1 2X 1 2X 1 1 1 1 1 1 1 1 0 1 2X X 1 X 2X 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 2 X 1 2X+1 X+1 0 2 1 0 2X+1 X+2 2X+1 2 0 2X+1 1 X+2 2X X+2 1 2X 1 2X+1 2X 1 1 2 1 0 1 1 2X+1 X 2 2X+2 2X+1 2 1 X+2 1 2X+2 X+1 2 0 X+1 2X X+2 1 1 2X+2 1 1 2X 1 1 2X+2 2X+2 2X+1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 X 2X 2X 0 2X 0 2X X 2X 2X 0 0 X X X 0 0 X 2X X X 2X 2X 2X 2X X 0 X X 2X X X 2X 0 2X 2X 0 0 2X X X 2X 2X X 2X 2X X 2X 0 X 0 X 2X 0 2X 2X 2X X 2X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X X 2X 0 0 X X 2X 0 2X 2X 2X 0 2X 0 0 X 0 2X 2X 0 X 0 X 2X X X 0 X 0 X 2X 2X X 0 X 0 X 0 X X X X X 2X 0 2X X X 0 X X 0 2X 2X 0 0 2X 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 2X 2X X 2X X 2X 2X X X X 2X X 2X X 2X 2X X X 0 X X X X X X 2X 2X 0 0 0 2X 2X 0 X X 2X 2X 0 2X 2X 0 2X 2X 0 2X X 2X 0 0 X 0 X 2X 0 2X 2X X 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 0 2X 2X X 0 X X X X X 2X 0 2X 2X 0 0 0 0 X 0 X 2X 2X X 0 2X 0 0 X 2X 2X 0 2X 0 0 2X 2X 0 2X X X 2X 0 0 X 2X X X X 2X X 0 0 2X X 2X X X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X X 2X 0 0 0 2X X X 2X 2X 2X 0 0 0 0 0 2X X 0 X 2X X 2X 2X 0 2X X 2X 2X 0 2X X 0 2X 0 0 X 2X 2X 2X 2X X X X X X 2X 2X 2X X 0 0 X 2X X 2X 2X 2X 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 X 2X 0 X X 2X 0 0 X 0 2X 2X 2X 2X 2X X 0 2X 0 2X 0 2X 0 2X X 0 X 0 0 0 X X X 0 2X 0 2X 0 0 2X 0 0 2X X X X X 2X 0 2X 2X X X 2X 0 2X 0 X X X
generates a code of length 80 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.
Homogenous weight enumerator: w(x)=1x^0+36x^135+188x^138+6x^140+334x^141+312x^143+564x^144+840x^146+722x^147+1758x^149+1194x^150+3222x^152+1874x^153+4842x^155+2506x^156+6936x^158+2792x^159+7356x^161+2964x^162+6498x^164+2458x^165+4338x^167+1682x^168+2202x^170+972x^171+780x^173+534x^174+246x^176+330x^177+30x^179+222x^180+160x^183+84x^186+34x^189+20x^192+8x^195+2x^198+2x^204
The gray image is a linear code over GF(3) with n=240, k=10 and d=135.
This code was found by Heurico 1.16 in 73.3 seconds.