The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+22x^24+40x^25+34x^26+40x^27+27x^28+18x^29+22x^30+16x^31+7x^32+4x^33+7x^34+8x^35+7x^36+2x^37+1x^42

The gray image is a code over GF(2) with n=56, k=8 and d=24.
This code was found by Heurico 1.16 in 0.00572 seconds.