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.