The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 X X 0 1 1 1 0 0 X 0 X 1 1 0 1 1 1 X 1 1 1 0 1 1 1 1 0 X 1 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 X 0 X 0 X X 1 1 1 1 X+1 1 X+1 1 1 1 1 X X+1 1 X+1 0 1 1 X 1 1 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 1 1 1 X+1 1 X+1 1 1 1 X X+1 X 1 0 0 X 1 0 X 1 X+1 X+1 X X 0 X+1 X 1 1 1 X 0 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 X X X 0 1 X X+1 1 1 1 1 0 X X 1 X X+1 X+1 0 0 X 1 1 X+1 X+1 X 0 0 0 1 0 1 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 X 0 X 0 0 X X+1 X+1 X 1 0 X+1 0 X X X+1 X+1 X 0 X+1 1 X+1 X+1 1 X+1 1 1 0 X+1 X+1 1 0 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 X X X+1 X X+1 X+1 X+1 1 1 0 1 0 X 0 X 0 X X+1 0 0 X 1 X 0 X 1 1 X 1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 1 X+1 X X+1 X 0 0 1 0 X+1 X+1 1 0 1 X+1 X+1 1 1 0 X 1 0 X+1 X X X+1 1 X+1 X+1 1 X+1 X+1 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+67x^38+110x^39+272x^40+356x^41+495x^42+510x^43+656x^44+852x^45+933x^46+958x^47+1129x^48+1234x^49+1105x^50+1332x^51+1119x^52+1102x^53+945x^54+844x^55+663x^56+496x^57+469x^58+236x^59+227x^60+116x^61+74x^62+40x^63+27x^64+2x^65+6x^66+2x^67+2x^68+2x^69+1x^70+1x^74

The gray image is a linear code over GF(2) with n=100, k=14 and d=38.
This code was found by Heurico 1.10 in 7.97 seconds.