The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+25x^24+60x^25+57x^26+66x^27+60x^28+42x^29+40x^30+40x^31+39x^32+16x^33+14x^34+18x^35+16x^36+10x^37+4x^39+3x^40+1x^42

The gray image is a code over GF(2) with n=58, k=9 and d=24.
This code was found by Heurico 1.16 in 0.0151 seconds.