The generator matrix

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

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+31x^90+200x^91+74x^92+218x^93+91x^94+314x^95+86x^96+178x^97+72x^98+250x^99+57x^100+158x^101+48x^102+156x^103+22x^104+22x^105+9x^106+28x^107+10x^108+4x^110+10x^111+3x^112+2x^115+2x^116+1x^132+1x^142

The gray image is a linear code over GF(2) with n=388, k=11 and d=180.
This code was found by Heurico 1.16 in 1.05 seconds.