The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  X  1  0  1  1  0  0  X  0  X  1  0  0  0  1  X  1  1  1  1  0  X  0  1  1
 0  1  0  0  0  0  0  0  0 X+1  1  1 X+1  1  1 X+1  X  1  X  0  1  1  1  1 X+1  X  X  1  1  1 X+1  X  X  1  1  1  0  1  0
 0  0  1  0  0  0  1  1  1  1  1  X  1  X X+1  X  1  X X+1  0  0  X  1 X+1 X+1  1  1  0  1  1  X X+1  0 X+1  0  1  0  X  0
 0  0  0  1  0  1  1  0  1  0  X  X  1  X  X X+1 X+1  0 X+1  1  1  1 X+1 X+1  1  X X+1  1  X X+1  0  X X+1  1  X  0  1  X  0
 0  0  0  0  1  1  0  1  1 X+1  X  1  X X+1  1  0  X  X X+1 X+1  1  X X+1  0  1  1  X  1  0  0 X+1  0  X X+1  0  1 X+1 X+1  0
 0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  X  0  0  X  X  X  0  X  X  0  0  X  0  X  0  0  X  0  0  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  X  0  X  X  X  0  0  0  0  0  0  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  X  X  X  0  0  X  X  X  0  0  X  X  0  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  X  0  X  X  X  X  0  0  X  0  X  X  0  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+100x^28+120x^29+284x^30+326x^31+522x^32+638x^33+753x^34+946x^35+1076x^36+1268x^37+1360x^38+1502x^39+1340x^40+1372x^41+1092x^42+1020x^43+804x^44+608x^45+516x^46+266x^47+223x^48+86x^49+81x^50+34x^51+28x^52+4x^53+8x^54+2x^55+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 1.16 in 31.6 seconds.