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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+89x^82+4x^83+161x^84+28x^85+187x^86+84x^87+240x^88+140x^89+297x^90+140x^91+200x^92+84x^93+125x^94+28x^95+106x^96+4x^97+50x^98+32x^100+20x^102+16x^104+9x^108+2x^116+1x^152

The gray image is a linear code over GF(2) with n=360, k=11 and d=164.
This code was found by Heurico 1.16 in 1 seconds.