The generator matrix

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

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+164x^54+183x^56+178x^58+128x^60+104x^62+85x^64+75x^66+34x^68+42x^70+9x^72+10x^74+6x^76+2x^78+2x^80+1x^82

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 2.3 seconds.