The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+303x^28+532x^30+1466x^32+1612x^34+2897x^36+2648x^38+2963x^40+1864x^42+1321x^44+468x^46+237x^48+44x^50+23x^52+5x^56

The gray image is a linear code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.16 in 81.9 seconds.