The generator matrix

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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+56x^50+104x^51+144x^52+192x^53+229x^54+276x^55+237x^56+240x^57+255x^58+240x^59+242x^60+260x^61+241x^62+234x^63+244x^64+204x^65+197x^66+134x^67+96x^68+96x^69+64x^70+34x^71+25x^72+28x^73+12x^74+2x^75+2x^76+4x^77+2x^78+1x^80

The gray image is a linear code over GF(2) with n=120, k=12 and d=50.
This code was found by Heurico 1.10 in 0.734 seconds.