The generator matrix

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

generates a code of length 35 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+68x^23+219x^24+452x^25+709x^26+1124x^27+1585x^28+2170x^29+3010x^30+3856x^31+4776x^32+5398x^33+6052x^34+6342x^35+5994x^36+5748x^37+4940x^38+3924x^39+3153x^40+2224x^41+1445x^42+960x^43+605x^44+370x^45+218x^46+104x^47+51x^48+22x^49+10x^50+6x^51

The gray image is a code over GF(2) with n=70, k=16 and d=23.
This code was found by Heurico 1.10 in 88.5 seconds.