The generator matrix

 1  0  0  1  1  1 X^2+X  X  1  1  1 X^2 X^2  1  0  1  1  1  X  1  X X^2  1 X^2+X  1  1  X  1  1 X^2+X  1 X^2+X  1  1 X^2  X  1 X^2  1 X^2+X  1  0  1  1  1  1 X^2 X^2+X  1  1  1  0  1  1 X^2+X X^2  1  0  1  1  0 X^2+X  1  1  1  1  X  1  1  0  0  X X^2+X  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  0  1  1 X^2  1 X^2  1  1
 0  1  0  0  1 X+1  1 X^2 X^2+X+1 X+1 X^2+X  1  1 X^2  0  0  X X^2+X+1  1 X^2+X+1  1  1  1  0 X^2 X^2  1 X+1  X X^2+X X^2+X  1 X^2+1 X+1  1 X^2+X X^2+X+1  1  0 X^2  0  1  X X^2+1  1 X+1  X  1  1 X^2+X X^2+X+1  X X^2+X+1 X^2+X  1 X^2  X  1  1  0  1  1 X^2+1 X^2+X+1  0 X+1  1 X^2 X^2+X  1  1  1 X^2 X^2+1  1 X^2+X X^2  1 X+1 X^2+1 X^2+1  X X^2  1  1  X X+1  1 X^2+X+1  1 X^2 X^2+X  1  1  1 X^2+X  0
 0  0  1  1  1 X^2  1  1 X+1 X^2+X X^2+1 X^2+1 X^2+X  X  1 X^2+X+1 X^2 X^2+X+1 X^2+X+1 X^2 X^2  1 X+1  1  0  1 X^2+X  X  0  1  1 X+1 X^2+X  1  0  1 X^2+X X+1 X^2+X  1 X^2+X+1 X^2+X  X  X X^2+1 X^2+X  1 X^2+1 X^2+X+1 X^2+1  0  1 X^2+1 X^2 X^2+1  1 X+1 X^2+X+1 X^2+1 X^2+X X+1 X^2  X  1  0  0  0 X+1 X^2+1 X^2+X X^2+X  0  1  0 X^2  X  0  X  1 X^2 X^2+X+1 X^2+X X^2+X+1 X^2+X+1  X X^2 X^2+X+1 X^2+X+1  X  X X^2+1 X+1 X^2 X+1 X^2+1 X^2+X+1  X
 0  0  0  X X^2+X  0  X  X X^2+X  0 X^2+X X^2+X  0  0 X^2+X X^2+X X^2  0 X^2 X^2+X  X X^2  0  0 X^2+X X^2  X  X  X  X  0  X  0 X^2+X X^2+X X^2 X^2 X^2+X X^2  X  0 X^2 X^2+X  X X^2  X  0 X^2  X  0  0  X X^2 X^2 X^2+X X^2+X  X  0 X^2+X  X  0  0 X^2  X X^2  X  X X^2+X  X  X  X X^2+X X^2 X^2  X  0 X^2  X X^2+X  0 X^2  X  0 X^2+X X^2+X  X  0  X X^2 X^2+X X^2+X  0 X^2  X  0 X^2+X X^2+X
 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  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 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+106x^90+280x^91+318x^92+326x^93+389x^94+352x^95+363x^96+346x^97+263x^98+294x^99+183x^100+176x^101+184x^102+108x^103+97x^104+62x^105+74x^106+38x^107+38x^108+42x^109+19x^110+16x^111+6x^112+4x^113+5x^114+1x^116+4x^117+1x^120

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 1.8 seconds.