The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^25+198x^26+250x^27+319x^28+414x^29+507x^30+574x^31+599x^32+732x^33+808x^34+724x^35+658x^36+628x^37+536x^38+444x^39+310x^40+194x^41+112x^42+50x^43+29x^44+14x^45+13x^46+6x^47+2x^48+2x^50+2x^52

The gray image is a code over GF(2) with n=68, k=13 and d=25.
This code was found by Heurico 1.16 in 89.3 seconds.