The generator matrix

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

generates a code of length 98 over Z2[X]/(X^3) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+69x^90+167x^92+20x^93+187x^94+100x^95+261x^96+104x^97+320x^98+200x^99+206x^100+68x^101+116x^102+20x^103+66x^104+44x^106+42x^108+24x^110+12x^112+7x^114+12x^116+1x^118+1x^172

The gray image is a linear code over GF(2) with n=392, k=11 and d=180.
This code was found by Heurico 1.16 in 1.23 seconds.