The generator matrix

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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+188x^54+104x^56+282x^58+70x^60+122x^62+55x^64+102x^66+16x^68+54x^70+8x^72+16x^74+2x^76+4x^78

The gray image is a linear code over GF(2) with n=120, k=10 and d=54.
This code was found by Heurico 1.10 in 71.5 seconds.