The generator matrix

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

generates a code of length 75 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+744x^138+1566x^139+4152x^140+6196x^141+8868x^142+14334x^143+17298x^144+22008x^145+30804x^146+34300x^147+41034x^148+50130x^149+48432x^150+50694x^151+52698x^152+43346x^153+34506x^154+28224x^155+17774x^156+10974x^157+7416x^158+3386x^159+1296x^160+708x^161+214x^162+96x^163+66x^164+72x^165+12x^166+24x^167+24x^168+18x^169+12x^170+14x^171

The gray image is a linear code over GF(3) with n=675, k=12 and d=414.
This code was found by Heurico 1.16 in 613 seconds.