The generator matrix

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

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+34x^27+110x^28+242x^29+352x^30+470x^31+612x^32+788x^33+987x^34+1136x^35+1253x^36+1352x^37+1524x^38+1500x^39+1300x^40+1192x^41+1022x^42+770x^43+620x^44+466x^45+288x^46+174x^47+69x^48+52x^49+47x^50+12x^51+1x^52+4x^53+4x^54+2x^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 1.10 in 5.31 seconds.