The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  X  X  1  1  1  X  1  1  X  X  1  0  0  1  1  1  1  X  0  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  0  1 X+1  X  1  1  0  0  1  X  1  X  X  0  X  X  1  1  0  X
 0  0  1  0  1  1  0  1  0  1  1  X  0 X+1  1  0  X  X  1  1  0  1  X  0  1  0  1  0  0  X X+1  X  1  0
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  0  1  1  1 X+1  0  X  0 X+1  X  1 X+1  1  X X+1  X  0  1  1  0  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  X  X  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  0  X  X  0  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  0  X  0  X  0  0  0  0  0  X  0  0  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+41x^24+62x^25+155x^26+220x^27+310x^28+428x^29+489x^30+614x^31+666x^32+704x^33+746x^34+740x^35+701x^36+652x^37+526x^38+408x^39+276x^40+194x^41+123x^42+64x^43+44x^44+8x^45+9x^46+2x^47+7x^48+1x^52+1x^56

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 3.48 seconds.