The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+128x^24+100x^26+110x^28+54x^30+67x^32+32x^34+14x^36+6x^38

The gray image is a code over GF(2) with n=56, k=9 and d=24.
This code was found by Heurico 1.16 in 0.0222 seconds.