The generator matrix

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

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+78x^89+190x^90+200x^91+356x^92+240x^93+381x^94+218x^95+366x^96+202x^97+401x^98+170x^99+384x^100+170x^101+267x^102+120x^103+150x^104+64x^105+31x^106+28x^107+12x^108+6x^109+8x^110+22x^111+4x^112+8x^113+2x^114+10x^115+4x^116+3x^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 2.06 seconds.