The generator matrix

 1  0  0  1  1  1  X  1  1  0  0  X  1  1  1  0  1  1  1  0  X  X  1  1  1  0  1  X  1  1  1  1  X  0  1  1  0  0  0  1  1  0  1  X  X  1  X  0  1  1  1  0  X  1  X  1  0  1  0  0
 0  1  0  0  1  1  1  0  X  X  1  1  1 X+1  0  1  1  X  1  1  0  1  X  1  0  X X+1  1  0  X  X  0  1  1  1  X  X  0  0 X+1  0  1  0  1  0  1  1  0  1  X  0  1  1  X  1 X+1  1  X  0  1
 0  0  1  1  1  0  1  X X+1  1  0  1 X+1  X  0 X+1 X+1  1  X  0  1  1  1  X  0  1  1  X X+1  1  X X+1 X+1  X X+1  0  1  1  1 X+1  1  X  1  1  1  0  X  X X+1 X+1  1  0  0  X X+1  1  0  1  1  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  X  0  0  X  0  X  X  X  X  0  X  X  0  0  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  0  X  X  0  X  X  X  X  0
 0  0  0  0  X  0  0  X  X  X  X  X  X  X  X  0  X  X  X  X  X  X  0  0  0  0  X  0  X  X  0  0  0  X  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  X  0  0  X  0  0  0  0  X  X  0  0  0  X  X  X  0  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  0  0  X  0  X  X  0  0  0  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+36x^54+40x^55+36x^56+66x^57+65x^58+56x^59+31x^60+30x^61+26x^62+20x^63+14x^64+14x^65+17x^66+8x^67+7x^68+14x^69+9x^70+4x^71+5x^72+6x^74+2x^76+4x^77+1x^78

The gray image is a linear code over GF(2) with n=120, k=9 and d=54.
This code was found by Heurico 1.16 in 0.047 seconds.