The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+80x^23+241x^24+308x^25+570x^26+810x^27+1192x^28+1484x^29+1774x^30+2370x^31+2712x^32+3098x^33+3270x^34+3078x^35+2784x^36+2528x^37+2068x^38+1548x^39+1055x^40+704x^41+430x^42+286x^43+200x^44+68x^45+78x^46+18x^47+7x^48+2x^49+2x^50+2x^51

The gray image is a linear code over GF(2) with n=68, k=15 and d=23.
This code was found by Heurico 1.16 in 95.5 seconds.