The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  1  0  0  1  1  2  2  1  1  1  1  0  1  2  2  1  2  1  0  0  2  2
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  2  2  2  1  1  3  1  1  2  2  1  1  0  3  0  0  0  1  1  1
 0  0  1  0  0  0  1  1  1  1  3  2  0  0  1  3  1  1  0  3  2  3  0  1  2  0  0  2  1  3  2  3  0  0
 0  0  0  1  0  1  1  0  3  1  2  3  0  3  0  3  2  2  0  1  1  2  3  0  0  3  1  0  0  1  2  2  0  1
 0  0  0  0  1  1  0  1  1  2  2  0  3  1  0  2  1  1  2  3  2  0  3  0  1  2  1  0  1  3  1  2  1  2
 0  0  0  0  0  2  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  0  0  0  0

generates a code of length 34 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+83x^26+128x^27+188x^28+248x^29+264x^30+310x^31+311x^32+352x^33+322x^34+348x^35+361x^36+320x^37+284x^38+200x^39+144x^40+96x^41+67x^42+36x^43+18x^44+8x^45+4x^46+2x^47+1x^52

The gray image is a code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.16 in 0.908 seconds.