The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2  1  0 X^2  1  1  0 X^2+X  1  1  X X^2+X  1  1  1  1  X  1 X^2+X X^2+X  1  1  1 X^2  1  X  1 X^2  1 X^2  1  1 X^2+X X^2  1  X X^2  X  1  1  1  1  1 X^2  0  1  1  X  0  1  1 X^2+X  X  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1  1  1 X^2+X  1  1  1  0  1  1  1  1  1  0  1  X  1  X  1  1 X^2  1  1  1
 0  1  0  0  X  X X^2+X  0  1 X^2+1  1  1  1  1 X^2+X+1 X^2+X X^2+X  1  0 X^2+X  1  0  0 X^2+1  1 X^2+1 X^2 X+1  1  0 X^2 X^2  0  1 X^2+1 X^2+X X^2  1 X^2+X+1  1  X  1  X  1 X+1  1  1 X^2+X X^2+X  X X^2 X^2+X+1  1 X^2  1 X+1 X^2+X+1  1  0 X+1  X  0  X  1 X^2+X  X  X X^2 X+1  1 X^2+X X^2+X+1  1  0 X^2+X X^2+1 X^2+X+1 X^2 X^2 X+1 X^2+X+1  1  X X^2  0 X^2+1 X^2+X  1 X^2+X+1 X^2 X+1  X X^2 X^2+X X^2 X^2+X+1 X^2+1 X^2
 0  0  1  0  X X^2+X+1 X^2+X+1  1 X+1 X+1 X^2  0 X+1 X^2+X+1  X X^2+X X^2+X X+1 X+1 X^2  1  1 X^2+X+1 X^2 X^2+1  1  1 X^2  0 X^2  1  X X^2+X  X X^2+X  1 X^2+X+1  1 X^2+1  X X^2+1  X  1 X+1 X^2+X+1  X  1  1 X^2 X^2+X+1 X^2+1  1 X^2+X  1  X X^2 X+1 X^2+X+1 X^2 X^2+X X^2  1 X^2  0  1  1  0 X+1 X+1  1 X^2+X+1 X^2+1 X^2 X^2+1  1  0 X^2  1 X^2+X+1 X^2+1  X  0  1 X^2+X+1 X^2+X+1 X^2 X^2+X X+1 X^2+1  1 X^2  1  0 X^2+X  X  X X^2+X X^2+X+1
 0  0  0  1 X+1 X^2+X+1  X  1  X X^2+X+1 X^2+X+1 X^2+X X^2+X  1  1 X^2  1 X^2+X+1 X^2+1 X+1 X^2+X X^2 X^2 X^2+1 X^2+1  0 X^2+X+1 X^2 X^2+X  1  1 X^2+1  X X^2+1  1 X^2+X+1 X^2+X X^2 X^2 X^2+X+1  0  0  X X^2  1  X X^2+1 X^2+1 X^2+X  0 X^2+X+1 X+1 X+1  0  X  X  0  0  1 X^2+1 X^2+X+1  X  1  0 X^2+X  1 X^2+1 X^2+X+1 X+1 X^2+X+1  0 X^2+X X^2 X^2+X+1  X X^2+X+1  0  1  X X^2+1 X^2  X X^2+1  1 X^2+X X^2+1  X  1  0  0  X X^2+X+1  0  X  1  X X^2+1 X^2+X+1
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  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+177x^90+288x^91+609x^92+524x^93+593x^94+586x^95+817x^96+568x^97+617x^98+478x^99+614x^100+380x^101+417x^102+362x^103+316x^104+176x^105+214x^106+122x^107+129x^108+68x^109+58x^110+20x^111+34x^112+8x^113+4x^114+8x^116+4x^117

The gray image is a linear code over GF(2) with n=392, k=13 and d=180.
This code was found by Heurico 1.16 in 5.54 seconds.