The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+121x^24+12x^26+365x^28+262x^30+1020x^32+1224x^34+2461x^36+2466x^38+3393x^40+1644x^42+1995x^44+458x^46+671x^48+64x^50+159x^52+14x^54+42x^56+12x^60

The gray image is a linear code over GF(2) with n=78, k=14 and d=24.
This code was found by Heurico 1.16 in 15.4 seconds.