The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+115x^24+156x^25+412x^26+612x^27+886x^28+1046x^29+1535x^30+1918x^31+2255x^32+2858x^33+2848x^34+3148x^35+3030x^36+2928x^37+2462x^38+1940x^39+1537x^40+1164x^41+834x^42+396x^43+340x^44+154x^45+97x^46+46x^47+28x^48+14x^49+2x^50+4x^51+2x^54

The gray image is a code over GF(2) with n=70, k=15 and d=24.
This code was found by Heurico 1.10 in 22.1 seconds.