The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+180x^83+110x^84+256x^85+87x^86+298x^87+73x^88+242x^89+39x^90+220x^91+90x^92+132x^93+95x^94+84x^95+9x^96+52x^97+1x^98+40x^99+3x^100+20x^101+2x^102+10x^103+2x^105+1x^116+1x^120

The gray image is a linear code over GF(2) with n=356, k=11 and d=166.
This code was found by Heurico 1.16 in 0.824 seconds.