The generator matrix

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

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+70x^23+231x^24+364x^25+577x^26+800x^27+1182x^28+1454x^29+1906x^30+2276x^31+2619x^32+3098x^33+3126x^34+3228x^35+2884x^36+2464x^37+2036x^38+1562x^39+1099x^40+740x^41+493x^42+228x^43+166x^44+66x^45+50x^46+28x^47+10x^48+6x^49+4x^50

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 55.1 seconds.