The generator matrix

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

generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+61x^42+154x^43+361x^44+510x^45+762x^46+1000x^47+1289x^48+1682x^49+2019x^50+2514x^51+3151x^52+3534x^53+3949x^54+4510x^55+4705x^56+4806x^57+4746x^58+4508x^59+4120x^60+3760x^61+3176x^62+2636x^63+2125x^64+1670x^65+1240x^66+874x^67+631x^68+366x^69+261x^70+174x^71+117x^72+50x^73+37x^74+14x^75+9x^76+6x^77+4x^78+3x^80+1x^82

The gray image is a linear code over GF(2) with n=114, k=16 and d=42.
This code was found by Heurico 1.11 in 194 seconds.