The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+91x^24+174x^25+323x^26+460x^27+580x^28+726x^29+1027x^30+1118x^31+1281x^32+1540x^33+1568x^34+1598x^35+1346x^36+1286x^37+1000x^38+802x^39+573x^40+336x^41+277x^42+110x^43+90x^44+28x^45+29x^46+8x^47+6x^48+6x^49

The gray image is a linear code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.16 in 26.9 seconds.