The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  X  1  X  0  0  1  0  X  0  1  1  1  1  1  1  1  X  0  1  1
 0  1  0  0  0  0  0  0  0 X+1  1  1 X+1  1  1 X+1  X  1  1  0  X  1  1  1  0  X  X  1  0  X  X  X  X  0
 0  0  1  0  0  0  1  1  1  1  1  X  1  X X+1  X  1  X X+1  X  1 X+1 X+1  0 X+1  X  1 X+1  1  0  1  1 X+1 X+1
 0  0  0  1  0  1  1  0  1  0  X  X  1  X  X X+1  X X+1  1  X X+1  0 X+1 X+1  X  X  0  1  1 X+1  1  0  1  1
 0  0  0  0  1  1  0  1  1 X+1  X  1  X X+1  1  0  1  X  0 X+1  X  X X+1  1  0 X+1  0  1  1 X+1  1  1  X  X
 0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  X  X  0  X  X  0  X  0  0  X  X  0  0  X  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0  X  0  0  X  0  0  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  0  X  X  0  0  0  X  X  0  0  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  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+127x^24+156x^25+306x^26+410x^27+584x^28+744x^29+1001x^30+1236x^31+1321x^32+1516x^33+1456x^34+1520x^35+1396x^36+1316x^37+1038x^38+836x^39+571x^40+328x^41+254x^42+86x^43+92x^44+36x^45+33x^46+8x^47+4x^48+8x^50

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 25.6 seconds.