The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  X  1  1  0  1  X  1  1  1  1  1  1  1  0  0  1  X  X  0  1  0  1  X
 0  1  0  0  0  0  0  X  1  1 X+1  1 X+1  0  1  X  0  1  1  0  1 X+1  X  0  1  0  X  X  1  0  0  1  0  1
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  1  1  1  0  X  1  X  0 X+1  X  X  1 X+1  0  1  1 X+1 X+1  X  0
 0  0  0  1  0  0  0  0  0  0  0  0  0 X+1  X  1 X+1  X  X  0 X+1 X+1 X+1  0  1  X  1  1  X X+1 X+1  0  0  X
 0  0  0  0  1  0  0  1 X+1  X  X  1  0  1 X+1  0  1  1 X+1 X+1  0 X+1 X+1  X  X  0  0  0  1  1  1  0 X+1  0
 0  0  0  0  0  1  0  1  X X+1  0  1  X  0  0  1  1  X  1  1 X+1 X+1  X X+1  0 X+1  1  X X+1  1  X  1  X  0
 0  0  0  0  0  0  1  1  0  X X+1 X+1  X  X  X  X  0 X+1  0 X+1  0 X+1 X+1  X  1  1  1  X  0  1  X  X  0  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+114x^24+142x^25+322x^26+466x^27+586x^28+770x^29+927x^30+1136x^31+1301x^32+1534x^33+1600x^34+1596x^35+1424x^36+1260x^37+954x^38+760x^39+566x^40+354x^41+262x^42+130x^43+102x^44+34x^45+31x^46+8x^47+2x^48+2x^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 18.9 seconds.