The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  X  X  X  X  X  1  1  1  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  X  0  X  X  0  X  0  0  X  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  0  0  X  X  X  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  X  X  0  X  X  0  X  X  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  0  X  0  0  X  0  X  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  X  0  X  X  0  0  X  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0  0  0  X  X  0  0  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  0  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  0  X  X  X  X  0  0  X  X  X  0  0  0  0  X

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+101x^28+8x^30+257x^32+128x^34+416x^36+240x^38+424x^40+128x^42+226x^44+8x^46+86x^48+24x^52+1x^60

The gray image is a linear code over GF(2) with n=76, k=11 and d=28.
This code was found by Heurico 1.16 in 0.419 seconds.