The generator matrix

 1  0  0  0  0  1  1  1  X  1  1  0  1  X  0  1  1  1  X  1  0  1  1  1  1  1  X  X  1  X  X  X  1  0  X  0  1  1  0  1  1  0  1  X  0  0  0  X  0  1  X  1  1  0  0  0  X  1  1  0
 0  1  0  0  0  X  X  X  0 X+1  1  1 X+1  1  1 X+1 X+1  0  1  X  X  X  1 X+1  0 X+1  1  1  0  0  0  1  0  X  X  1 X+1 X+1  X  X  1  1  0  X  1  1  0  1  1  1  1  0  1  0  0  1  X  1  0  X
 0  0  1  0  0  0  0  0  0  0  0  X  X  X  0  X X+1  1  1  1  1 X+1 X+1 X+1  1  1 X+1 X+1  X  X  1  1  X  1  0  0 X+1  X  1  X X+1  0  1  X  0 X+1  1  1  X  X  1  0  1  1  0  X  1  0  X  1
 0  0  0  1  0  0 X+1  1  1  0  X  0  1 X+1 X+1 X+1 X+1  1  X  X X+1 X+1  0  1  X  X X+1  1  0  X  0  0  1  0  1  X  0 X+1  1  0  1  1 X+1  X  X  1  0  1  X X+1  0  X  1  0  1  0  0  X  X X+1
 0  0  0  0  1  1 X+1  0  1  X X+1 X+1  X  1  X X+1  1 X+1  X X+1  1  X X+1  0  X  0  0  1  1  1  0  1  0  0  X  0  1  1 X+1  X  0 X+1  1  1  1 X+1  X  1  0  X  X  0  X X+1  X  1  1  X  0 X+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+168x^54+208x^56+138x^58+141x^60+84x^62+87x^64+78x^66+52x^68+36x^70+20x^72+4x^74+3x^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 1.16 in 46.9 seconds.