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

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+100x^90+8x^91+166x^92+52x^93+209x^94+92x^95+261x^96+108x^97+232x^98+116x^99+173x^100+76x^101+135x^102+36x^103+92x^104+20x^105+53x^106+4x^107+49x^108+36x^110+24x^112+3x^114+1x^120+1x^160

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 1.27 seconds.