The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+66x^38+116x^39+257x^40+334x^41+469x^42+556x^43+746x^44+766x^45+941x^46+1124x^47+994x^48+1190x^49+1183x^50+1154x^51+1152x^52+1132x^53+927x^54+892x^55+693x^56+570x^57+395x^58+224x^59+234x^60+102x^61+104x^62+28x^63+15x^64+2x^65+9x^66+2x^67+4x^68+1x^70+1x^78

The gray image is a linear code over GF(2) with n=100, k=14 and d=38.
This code was found by Heurico 1.16 in 48 seconds.