The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+92x^82+36x^83+234x^84+84x^85+277x^86+92x^87+240x^88+92x^89+158x^90+92x^91+206x^92+76x^93+196x^94+36x^95+63x^96+4x^97+37x^98+22x^100+7x^102+2x^124+1x^130

The gray image is a linear code over GF(2) with n=356, k=11 and d=164.
This code was found by Heurico 1.16 in 0.711 seconds.