The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+56x^46+92x^47+148x^48+196x^49+207x^50+234x^51+244x^52+226x^53+255x^54+270x^55+255x^56+300x^57+269x^58+248x^59+234x^60+224x^61+163x^62+148x^63+113x^64+64x^65+65x^66+30x^67+24x^68+14x^69+5x^70+2x^71+3x^72+3x^74+2x^76+1x^78

The gray image is a linear code over GF(2) with n=112, k=12 and d=46.
This code was found by Heurico 1.16 in 1.89 seconds.