The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+143x^48+198x^50+202x^52+102x^54+96x^56+78x^58+106x^60+50x^62+24x^64+12x^66+4x^68+8x^70

The gray image is a linear code over GF(2) with n=108, k=10 and d=48.
This code was found by Heurico 1.10 in 0.078 seconds.