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 X X X X X X X 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 0 X 0 X X X 0 0 X X 0 X X X X X X 0 0 0 0 0 0 X 0 X X X 0 0 0 0 X 0 X X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 0 X X X X 0 0 0 X X 0 X X 0 0 0 X X X X 0 0 0 X X X X 0 0 0 0 0 X X X X 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 X X 0 0 X X 0 X X 0 0 0 X X 0 X X 0 0 X X 0 X X 0 0 X X 0 0 0 X X 0 0 X X
generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+7x^54+16x^55+7x^56+1x^78
The gray image is a linear code over GF(2) with n=108, k=5 and d=54.
This code was found by Heurico 1.16 in 0.02 seconds.