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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+68x^45+135x^46+176x^47+206x^48+276x^49+246x^50+350x^51+499x^52+384x^53+347x^54+318x^55+344x^56+228x^57+112x^58+142x^59+84x^60+52x^61+53x^62+34x^63+15x^64+16x^65+2x^66+4x^67+1x^68+1x^70+2x^72

The gray image is a linear code over GF(2) with n=212, k=12 and d=90.
This code was found by Heurico 1.16 in 4.2 seconds.