The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+82x^25+167x^26+246x^27+348x^28+404x^29+487x^30+590x^31+657x^32+690x^33+746x^34+744x^35+705x^36+660x^37+533x^38+400x^39+289x^40+186x^41+106x^42+66x^43+47x^44+24x^45+8x^46+2x^47+1x^48+2x^49+1x^50

The gray image is a code over GF(2) with n=68, k=13 and d=25.
This code was found by Heurico 1.10 in 1.5 seconds.