The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+218x^24+88x^26+260x^28+88x^30+235x^32+72x^34+44x^36+8x^38+10x^40

The gray image is a code over GF(2) with n=58, k=10 and d=24.
This code was found by Heurico 1.16 in 6.55 seconds.