The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  0  X  1  0  0  0  1  1  X  1  X  1  X  1  0  1  0  0  0  1  X  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0  1  1  1  1  0  X  0  X  X  1  0  1  1  X  X  0  X  1 X+1  X  0
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  X X+1 X+1  X  1 X+1 X+1  1  X  1 X+1 X+1  X  X  X  X  1  1  1  1  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  X  1 X+1  0  X  1  X  0  X  X  1  1 X+1  0  X  1  1  X  0  0  0
 0  0  0  0  1  0  1  1  0  1  0  1  X  X  0 X+1 X+1 X+1 X+1  0  0  0  0  X  0  X  1 X+1  1  1  0  1 X+1  X
 0  0  0  0  0  1  1  0  1  1  X X+1  X  1  1  1 X+1  1 X+1  0  1  1 X+1  0  0 X+1  0  X  0  1  0  1 X+1  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  X  0  X  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  0  X  X  X  0  0  0  0  X  X  0  0  X  0  X  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+60x^23+235x^24+342x^25+549x^26+912x^27+1076x^28+1486x^29+1936x^30+2218x^31+2730x^32+3064x^33+3140x^34+3160x^35+2965x^36+2484x^37+2016x^38+1544x^39+1013x^40+718x^41+509x^42+264x^43+158x^44+94x^45+40x^46+34x^47+13x^48+4x^49+2x^50+1x^52

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 48.1 seconds.