The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+78x^25+176x^26+258x^27+299x^28+418x^29+553x^30+558x^31+598x^32+700x^33+866x^34+736x^35+570x^36+636x^37+580x^38+432x^39+280x^40+198x^41+126x^42+62x^43+42x^44+18x^45+3x^46+2x^47+1x^48+1x^60

The gray image is a linear code over GF(2) with n=68, k=13 and d=25.
This code was found by Heurico 1.16 in 3.97 seconds.