The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+50x^24+127x^26+24x^27+194x^28+130x^29+341x^30+358x^31+594x^32+726x^33+905x^34+1210x^35+1149x^36+1620x^37+1348x^38+1660x^39+1296x^40+1260x^41+923x^42+716x^43+601x^44+330x^45+338x^46+126x^47+164x^48+30x^49+91x^50+2x^51+39x^52+20x^54+6x^56+2x^58+1x^60+1x^62+1x^64

The gray image is a linear code over GF(2) with n=76, k=14 and d=24.
This code was found by Heurico 1.16 in 16.8 seconds.