The generator matrix

 1  0  0  0  0  0  1  1  1  1  X  0  1  1  1  1  1  1  1  1  1  1  X  0  1  X  1  1  1  0  X  X  1  1  1  X  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  1 X+1 X+1  1  X  X  X X+1  1  1  X X+1  0  1 X+1  0  1  1  X X+1  1 X+1  X  1  1  0
 0  0  1  0  0  0  0  0 X+1  1  1  0  X  X  X  X X+1  1  1  0 X+1  0  0  1 X+1  1  1 X+1  0  1  0  0  1  X  X  X X+1  0  0
 0  0  0  1  0  0  0  1  1  0 X+1  X  0  X X+1  1 X+1  0  X  0  1  1  0  1  X  X  1  1  1  1  0  1  1 X+1 X+1  X  1  1  0
 0  0  0  0  1  0  1  1  0 X+1  1 X+1  1  X  X  X  1  1  0  X X+1  1  0  X  1  1  X  X  0 X+1 X+1 X+1  0  X  0  1  1  0  0
 0  0  0  0  0  1  1  0 X+1  X X+1  1  0 X+1  X X+1 X+1  1 X+1  0  X  X  1  0 X+1  1  0  1  X  X  1  0  1 X+1  1  1  0  1  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  0  X  X  0  X  0  0  0  X  0  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  X  X  0  X  0  0  X  X  0  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+85x^28+88x^29+295x^30+368x^31+553x^32+604x^33+839x^34+922x^35+1052x^36+1314x^37+1219x^38+1494x^39+1278x^40+1410x^41+1156x^42+1034x^43+873x^44+598x^45+481x^46+242x^47+238x^48+74x^49+91x^50+36x^51+14x^52+8x^53+13x^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 1.16 in 32.6 seconds.