The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+59x^26+46x^27+177x^28+134x^29+325x^30+368x^31+603x^32+746x^33+931x^34+1198x^35+1267x^36+1612x^37+1432x^38+1600x^39+1272x^40+1188x^41+1009x^42+730x^43+615x^44+398x^45+282x^46+144x^47+136x^48+18x^49+49x^50+10x^51+21x^52+8x^54+4x^56+1x^62

The gray image is a linear code over GF(2) with n=76, k=14 and d=26.
This code was found by Heurico 1.16 in 15.8 seconds.