The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  X  1  1  X  X  0  1  1  X  1  1  0  1  0  1  1  0  X  0  0  1  1  0  0  X  1  1  1
 0  1  0  0  0  0  0  X  1  1 X+1  1 X+1  0  1  1  0  X  X  0 X+1 X+1  1  0  1  0 X+1  X  0  X  1  X  0  0  1  1  X  0  0
 0  0  1  0  0  0  0  0  0  0  0  0 X+1  1  1  1  X  0  1  1  X  1  X  X X+1  0  X  1  1  1  1  X  1  1  0  0  X  1  0
 0  0  0  1  0  0  0  0  0  0  0  0  0  X  1 X+1  1 X+1  X X+1 X+1  1  X  0  1  X  1  X  0  1  X  X X+1  1  X  1 X+1  1  0
 0  0  0  0  1  0  0  1 X+1  X  X  1  0 X+1  1 X+1  0  0  X  1  1 X+1 X+1 X+1  X  1  0 X+1  X  0  1  0  1  1  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  1 X+1  X X+1  1  0 X+1  1  0  0  1 X+1 X+1  0  0  X  1  X X+1  0  0
 0  0  0  0  0  0  1  1  0  X X+1 X+1  X  X  0  1 X+1  X X+1  X  1  1  0 X+1  0  0  X  1 X+1 X+1  X X+1  X  1  X  1  X  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+73x^28+108x^29+335x^30+356x^31+540x^32+574x^33+751x^34+1000x^35+1027x^36+1288x^37+1297x^38+1440x^39+1318x^40+1454x^41+1252x^42+1022x^43+765x^44+542x^45+487x^46+242x^47+219x^48+124x^49+93x^50+34x^51+23x^52+6x^53+9x^54+2x^55+2x^56

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 18.9 seconds.