The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+120x^26+391x^28+557x^30+625x^32+706x^34+674x^36+546x^38+324x^40+108x^42+31x^44+9x^46+2x^48+2x^50

The gray image is a linear code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.16 in 0.966 seconds.