The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+58x^89+169x^90+258x^91+291x^92+276x^93+341x^94+346x^95+288x^96+320x^97+275x^98+250x^99+271x^100+258x^101+204x^102+148x^103+98x^104+80x^105+54x^106+20x^107+30x^108+6x^109+9x^110+10x^111+6x^112+6x^113+4x^114+4x^115+4x^116+4x^117+4x^119+2x^124+1x^128

The gray image is a linear code over GF(2) with n=388, k=12 and d=178.
This code was found by Heurico 1.16 in 1.84 seconds.