The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+76x^90+254x^91+368x^92+360x^93+437x^94+336x^95+357x^96+280x^97+309x^98+212x^99+196x^100+182x^101+177x^102+120x^103+104x^104+72x^105+79x^106+50x^107+33x^108+34x^109+26x^110+20x^111+4x^112+8x^114+1x^116

The gray image is a linear code over GF(2) with n=388, k=12 and d=180.
This code was found by Heurico 1.16 in 1.29 seconds.