The generator matrix

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

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+84x^54+57x^56+115x^58+24x^60+106x^62+37x^64+72x^66+2x^70+7x^72+5x^74+2x^88

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 2.98 seconds.