The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 0 1 X 1 1 1 0 1 1 1 1 1 1 X 0 X 0
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 X+1 0 1 X 1 X+1 X+1 X 1 X+1 0 0 1 1 1 X+1 0 1 0 X X+1 1 1 X+1 1 0 X X 1 X 1 X+1 1 X 1 1 1 1 1
0 0 X 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X X X X X X 0 0 X 0 X X X 0 0 X X 0 X 0 0 X 0 0 0 X 0 0 0 X 0 X 0 X 0 X
0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 0 0 0 X 0 X 0 X 0 X X X X X 0 0 X X 0 X X X X X X 0 0
0 0 0 0 X 0 0 0 0 0 X X X 0 X 0 X 0 X 0 X X X X 0 X 0 0 X 0 0 X X X 0 X X 0 0 X X X X X 0 0 0 X X 0 0 X X X
0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X 0 X 0 0 X X 0 0 0 0 0 0 0 0 X X 0 X X X 0 X 0 X 0 X X X X X 0 0 0 X 0 X X X
0 0 0 0 0 0 X 0 X X 0 0 X 0 X X X X X X X X 0 0 X X X X X X 0 X X 0 X 0 0 X X X 0 0 0 0 0 0 0 X 0 0 X X 0 X
0 0 0 0 0 0 0 X X 0 X 0 X 0 X 0 0 X 0 X X 0 0 0 X X X 0 0 0 0 0 X 0 X X X 0 X 0 X 0 X X X X 0 0 0 X X X 0 0
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+274x^48+224x^52+318x^56+160x^60+37x^64+10x^72
The gray image is a linear code over GF(2) with n=108, k=10 and d=48.
This code was found by Heurico 1.16 in 12.6 seconds.