The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2  1  X  1  1  X  1  1  1 X^2+2X  1  1  1 X^2+X  1 2X^2+2X  1  1  X  1  0 2X^2+X  1  1 X^2+X  1  0  1  1  1  1  1  1  0  1  1  1  1  1  1 X^2 2X  1 2X^2+X  1 X^2  1 2X^2+2X 2X  1  1 2X^2+2X  1  1  1 X^2  1 2X  1  0  1  1  1 2X^2+X 2X  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1 X+2  1 2X^2+X+2  1 2X^2+2  1 2X X+1  1 2X^2+X+2 X^2  1 2X^2+X X+1 X^2+2X+2  2  1 X^2+X  1 X^2+2X+1 2X+1  1 2X^2+X+2  1  X X^2+2X  X  1 X^2+2X+2  1 2X 2X^2+2X+2 2X^2+2  1  2 2X^2+2X+2  1 X^2+X+1 X^2+1 2X^2+2X+2 2X+1 2X+2 2X^2+2X+1  1  1 2X+2 X^2 2X^2+X+1  1 2X^2+2X  1  1  2 2X^2+2X+1  1 2X^2+X+2 2X^2+X+1 X^2+X  1 2X^2  1 2X^2+X+2  1  2 2X^2+2 2X^2+X+1  1  1 2X^2+2X
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 X^2+1 2X^2+2X 2X^2+1 2X^2+X+2 X+2 X+1 2X^2 2X^2+2X+1 X^2+X+2 2X^2+X X^2+X+1  1 2X^2+X+2  X X+1  X 2X^2+2  2 X^2+1 X^2 2X^2+2X+1 2X  1  1 X^2+2X+1  2 2X^2 X^2+X+2 2X^2+X+2 2X^2 2X^2+1 2X  2 2X^2+2 2X+1 2X^2+2 2X^2+2X 2X^2+X+2 2X+1 X^2+1  0  0  X 2X^2+X X^2+2X+2  1 X^2+X+1 2X+1 X+1 2X^2+X+2 2X^2 2X^2+2X X^2+2X+2  2 2X^2 2X^2+X+2 X+2 X+1 X+1 2X^2+2X+1 X+1 X^2+X+2 2X^2+X+2  2 2X^2+X+1 X^2+X+1 2X^2+X+1 2X^2+X
 0  0  0 2X 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2+X X^2+X 2X^2+X 2X^2+X X^2+2X 2X^2+2X  X X^2+2X X^2+2X 2X X^2+2X 2X^2+2X  X  X X^2+2X X^2+2X 2X^2+X 2X^2+X 2X^2+X  0 2X X^2+2X 2X X^2+2X  X 2X^2+2X X^2+X X^2+X 2X^2+2X X^2+2X 2X^2+2X X^2 2X^2 2X^2+X 2X  0 2X X^2 X^2+X X^2+2X 2X^2+2X 2X^2+X  X 2X^2+X 2X^2 X^2+2X X^2+X  X 2X  X  X X^2+2X X^2 X^2 X^2  X  0  0 2X^2+X 2X^2+2X

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+482x^141+948x^142+1776x^143+3526x^144+5196x^145+5778x^146+8116x^147+9948x^148+11064x^149+14126x^150+16662x^151+16308x^152+17502x^153+17130x^154+14214x^155+12006x^156+8412x^157+5256x^158+3804x^159+2382x^160+906x^161+778x^162+384x^163+36x^164+68x^165+108x^166+42x^167+72x^168+42x^169+18x^170+18x^171+24x^172+6x^173+6x^174+2x^177

The gray image is a linear code over GF(3) with n=684, k=11 and d=423.
This code was found by Heurico 1.16 in 80.9 seconds.