The generator matrix

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

generates a code of length 34 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+34x^24+112x^25+158x^26+240x^27+324x^28+414x^29+501x^30+582x^31+631x^32+664x^33+753x^34+702x^35+702x^36+652x^37+519x^38+440x^39+309x^40+184x^41+101x^42+80x^43+39x^44+22x^45+16x^46+2x^47+5x^48+2x^51+3x^52

The gray image is a code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.10 in 1.42 seconds.