The generator matrix

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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+61x^48+90x^49+152x^50+210x^51+232x^52+238x^53+253x^54+240x^55+248x^56+262x^57+213x^58+274x^59+254x^60+242x^61+213x^62+210x^63+180x^64+150x^65+117x^66+76x^67+70x^68+38x^69+37x^70+14x^71+10x^72+2x^73+6x^74+2x^77+1x^86

The gray image is a linear code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.16 in 1.89 seconds.