The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+31x^30+30x^31+79x^32+64x^33+107x^34+136x^35+148x^36+192x^37+170x^38+180x^39+150x^40+192x^41+134x^42+136x^43+96x^44+64x^45+51x^46+30x^47+24x^48+15x^50+12x^52+4x^54+2x^56

The gray image is a linear code over GF(2) with n=78, k=11 and d=30.
This code was found by Heurico 1.16 in 0.337 seconds.