The generator matrix

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

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+81x^26+150x^27+187x^28+234x^29+260x^30+294x^31+330x^32+346x^33+327x^34+330x^35+333x^36+342x^37+282x^38+226x^39+161x^40+94x^41+68x^42+24x^43+12x^44+8x^45+5x^46+1x^54

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 0.918 seconds.