The generator matrix

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

generates a code of length 36 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+34x^23+128x^24+294x^25+505x^26+832x^27+1172x^28+1632x^29+2346x^30+3074x^31+3775x^32+4566x^33+5390x^34+5872x^35+6028x^36+5924x^37+5482x^38+4674x^39+3892x^40+3206x^41+2337x^42+1644x^43+1100x^44+684x^45+418x^46+234x^47+156x^48+78x^49+32x^50+20x^51+4x^52+2x^54

The gray image is a code over GF(2) with n=72, k=16 and d=23.
This code was found by Heurico 1.10 in 97 seconds.