The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  0  X  X  X  1  0  0  1  X  1  X  1  1  0  0  1  0  0  X  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  1  1  1  1  1  1  1  1  X  0  X  X X+1  0  1  1  1  1  X  0
 0  0  1  0  0  0  0  0  0  1  1  X X+1  1  1  1  0  1 X+1  0  X  0  X  X  1  1  0  X  0  0 X+1 X+1  0  0
 0  0  0  1  0  0  0  0  1  0  X X+1  1 X+1  1  1 X+1 X+1 X+1  X X+1  1  1  1  X X+1 X+1  1  0  0  1  0  1  0
 0  0  0  0  1  0  0  0  1  1  0 X+1  0  1 X+1  1  X  0  X  1  1  X  0  1  X  0  0  1  X  1 X+1  1  0  X
 0  0  0  0  0  1  0  1  0 X+1  X  X X+1  1 X+1  X X+1 X+1  0  X  X X+1  1  1  X  X  0  X  X  1  X  1  X X+1
 0  0  0  0  0  0  1  1 X+1  X X+1  X  X X+1  X  1  0  1  X  0  1  X X+1  1 X+1  0 X+1  0 X+1 X+1  X  X  1  1
 0  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  0  X  0  X  0  0  0  X  0  X  0  X  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+219x^24+362x^25+580x^26+778x^27+1174x^28+1446x^29+1930x^30+2326x^31+2643x^32+3114x^33+3117x^34+3224x^35+2864x^36+2472x^37+2032x^38+1510x^39+1099x^40+714x^41+482x^42+254x^43+178x^44+82x^45+46x^46+30x^47+14x^48+2x^49+5x^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 1.11 in 20 seconds.