The generator matrix

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

generates a code of length 99 over Z2[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+170x^90+116x^91+430x^92+264x^93+692x^94+424x^95+665x^96+472x^97+729x^98+520x^99+713x^100+472x^101+589x^102+424x^103+566x^104+264x^105+294x^106+116x^107+77x^108+62x^110+50x^112+39x^114+19x^116+13x^118+4x^120+4x^122+1x^128+1x^132+1x^136

The gray image is a linear code over GF(2) with n=396, k=13 and d=180.
This code was found by Heurico 1.16 in 7.83 seconds.