The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  0  X  X  1  0  0  0  1  X  1  0  1  X  0  X  1  1  X  X  1  0  1  1  0  X  1  1  0  X  X  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  0 X+1  1 X+1  1 X+1  1  1  1 X+1 X+1  1  0  1  X  1 X+1  1  X  1  0  1  X  1  1  0  0
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  0  0  X  1  1  1  1  1  1  1 X+1  0  1  X  X X+1  0 X+1 X+1  X  1  X  1  1 X+1  0  1  1  X  1  0  X  1 X+1  0  0
 0  0  0  1  0  0  0  0  0  X  X  1  1 X+1 X+1  1  1  0  0 X+1  X  1  0  1 X+1  X X+1 X+1  X  X  1  X  X X+1  0  1  1 X+1  X X+1  0  0  0  X X+1  1  X  0  1  0
 0  0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  X  1  1  X  0  1 X+1 X+1  0  X  0  X X+1  X X+1  1  X  X  1  X X+1  0  1 X+1 X+1  1  0 X+1  1  X  1  X  1  0
 0  0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  0  X X+1 X+1  X  X  1  0 X+1 X+1  X X+1  1  X  0  1  1 X+1  X  1  0  1  1 X+1  0  0  1  1 X+1  1  X  1  1  1  1  0
 0  0  0  0  0  0  1  1  X  1  1 X+1  X  1  X  1  X  1 X+1  1  X  X  X  1  X  1  0 X+1  X  X X+1 X+1  X  1  0  1  X  0  1  1  1  1 X+1 X+1  0 X+1  0  0  0  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+112x^39+280x^40+342x^41+469x^42+508x^43+733x^44+810x^45+903x^46+1108x^47+1025x^48+1242x^49+1155x^50+1172x^51+1121x^52+1106x^53+968x^54+856x^55+705x^56+548x^57+440x^58+248x^59+214x^60+100x^61+82x^62+28x^63+17x^64+12x^65+12x^66+1x^86

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 25.1 seconds.