The generator matrix

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

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+79x^28+92x^29+269x^30+302x^31+460x^32+662x^33+903x^34+956x^35+941x^36+1230x^37+1474x^38+1534x^39+1234x^40+1428x^41+1312x^42+1072x^43+686x^44+592x^45+553x^46+210x^47+157x^48+86x^49+87x^50+20x^51+21x^52+6x^53+8x^54+2x^55+4x^56+2x^58+1x^60

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.