The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+262x^84+320x^85+480x^86+296x^87+529x^88+276x^89+408x^90+236x^91+296x^92+112x^93+182x^94+116x^95+182x^96+84x^97+92x^98+44x^99+57x^100+32x^101+46x^102+12x^103+16x^104+8x^105+8x^106+1x^108

The gray image is a linear code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.11 in 1.38 seconds.