The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+26x^27+153x^28+174x^29+351x^30+508x^31+640x^32+836x^33+884x^34+1128x^35+1235x^36+1426x^37+1484x^38+1436x^39+1453x^40+1172x^41+940x^42+814x^43+623x^44+430x^45+283x^46+168x^47+111x^48+56x^49+24x^50+16x^51+5x^52+2x^53+2x^54+3x^56

The gray image is a linear code over GF(2) with n=76, k=14 and d=27.
This code was found by Heurico 1.16 in 31.7 seconds.