The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+85x^28+106x^29+283x^30+346x^31+542x^32+624x^33+801x^34+988x^35+1081x^36+1240x^37+1270x^38+1498x^39+1292x^40+1326x^41+1156x^42+1094x^43+871x^44+560x^45+471x^46+276x^47+203x^48+106x^49+105x^50+22x^51+19x^52+6x^53+8x^54+2x^56+2x^58

The gray image is a linear code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.10 in 5.53 seconds.