The generator matrix

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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+68x^49+171x^50+214x^51+305x^52+342x^53+385x^54+398x^55+450x^56+494x^57+516x^58+506x^59+528x^60+518x^61+485x^62+560x^63+417x^64+448x^65+366x^66+302x^67+263x^68+146x^69+103x^70+66x^71+76x^72+30x^73+18x^74+2x^75+8x^76+2x^77+2x^78+1x^82+1x^94

The gray image is a linear code over GF(2) with n=120, k=13 and d=49.
This code was found by Heurico 1.16 in 9.24 seconds.