The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+240x^85+134x^86+388x^87+110x^88+314x^89+101x^90+194x^91+54x^92+120x^93+42x^94+122x^95+32x^96+60x^97+21x^98+36x^99+8x^100+28x^101+6x^102+26x^103+1x^104+6x^105+2x^107+2x^112

The gray image is a linear code over GF(2) with n=360, k=11 and d=170.
This code was found by Heurico 1.16 in 3.3 seconds.