The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  X  1  1  X  X  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  0  0  X  X  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  0  0  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  X  0  0  0  0  X  0  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  X  X  X  0  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  0  X  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  0  X  X  X  X  0  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  X  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  X  X  0  X  0  X  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  0  X  X  0  0  X  0  0  X  X  0  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+82x^24+48x^26+20x^27+113x^28+80x^29+81x^30+160x^31+126x^32+240x^33+123x^34+264x^35+114x^36+176x^37+130x^38+64x^39+60x^40+16x^41+94x^42+4x^43+13x^44+29x^46+3x^48+7x^50

The gray image is a linear code over GF(2) with n=68, k=11 and d=24.
This code was found by Heurico 1.16 in 0.332 seconds.