The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  0 X^2+X  1  1  1  1  0  1  1 X^2+X  1  1  1  0  1 X^2+X  1 X^2  1  X  1  1  1  0  1 X^2+X  1  1  1  1 X^2+X  1  1 X^2  X  1  1  1  1  1  1  X X^2  0  1 X^2  1  0 X^2+X  1  0  1  X X^2+X  0 X^2  X X^2+X  X  1  1  X  1  0 X^2 X^2+X  X  0 X^2+X  1  0  1  1  1  1  1  1  1  1  1  1 X^2 X^2+X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+1  1 X^2+X  0 X+1  1  1 X^2+1 X^2+X X^2 X+1  1 X^2+X X^2+1  1  X  0 X^2+X+1  1 X^2+1  1 X^2+X  1 X+1  1 X^2+1  0 X^2+X  1 X^2+1  1 X+1  0 X^2+X X+1  1  1  0  1  1 X^2 X^2+1 X^2+X+1  X  1  X  1  1  X  X  1 X^2  1  1 X^2+X+1  1  0  1  1  1  1 X^2+X  1  1 X+1 X^2+X  1  X  1  1  1  1  1  1 X^2+X+1  1 X^2+1 X^2+1 X^2+X+1 X+1  0 X^2+1 X^2  1  X X^2+1  1  1
 0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 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 X^2  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2  0
 0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  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  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  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 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  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+53x^90+88x^91+239x^92+148x^93+198x^94+120x^95+214x^96+84x^97+130x^98+104x^99+204x^100+124x^101+94x^102+72x^103+100x^104+28x^105+33x^106+3x^108+3x^110+3x^112+1x^116+1x^120+1x^126+1x^132+1x^136

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 0.897 seconds.