The generator matrix

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

generates a code of length 32 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+79x^24+108x^25+172x^26+252x^27+256x^28+282x^29+357x^30+372x^31+344x^32+414x^33+323x^34+296x^35+267x^36+198x^37+159x^38+100x^39+76x^40+22x^41+11x^42+4x^43+1x^44+2x^50

The gray image is a code over GF(2) with n=64, k=12 and d=24.
This code was found by Heurico 1.16 in 0.802 seconds.