The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  1  X  1  0  1  X  0  1  X  X  1  X  1  1  X  1  1  1  0  X  X  0  1  X  X  1  1  1  1  1  1  0  1  1  1  1  1  X
 0  1  0  0  0  0  0  0  0  0  0  0  X  1 X+1  1  1  1 X+1  1 X+1  X  1  X  1  1 X+1  1  0 X+1  X  1  0  X  X  1  1  X  1  1  0  1  0  X X+1  1 X+1  1  1  X  X  0  0  1
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  0  0  X X+1 X+1 X+1 X+1  0  1  X X+1  0  1 X+1 X+1 X+1  X  1  1 X+1  X  1  0  1  X X+1  0  X  X  1  1  1  0  1 X+1  0  0 X+1  1  0  1
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  0 X+1  1  X X+1  0 X+1  1  1  0  X  1  0 X+1  0 X+1  0  X  1  X  0  X  X  1  1  1 X+1  X  1 X+1  X  1  0 X+1 X+1  1 X+1  X  1  1 X+1
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  X  1  1  0  X  1  1  0  0  1 X+1  X  1  X  0  X X+1  1  1 X+1  X  0  1 X+1  1  1 X+1  1  X  0  X  1  0  X X+1 X+1 X+1  0  X  X  X
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  1 X+1  0  0  0  1  1  X X+1 X+1  X X+1  X X+1  1  X  0  1  X  X X+1 X+1  X  0  0 X+1  1 X+1  1 X+1  0  0  X  1  1  1  1  0  1 X+1  0

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+90x^45+146x^46+206x^47+273x^48+238x^49+242x^50+240x^51+271x^52+268x^53+247x^54+256x^55+267x^56+248x^57+229x^58+240x^59+155x^60+138x^61+130x^62+74x^63+55x^64+34x^65+29x^66+8x^67+2x^68+8x^69+1x^78

The gray image is a linear code over GF(2) with n=108, k=12 and d=45.
This code was found by Heurico 1.16 in 69.1 seconds.