The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+19x^24+46x^25+31x^26+36x^27+33x^28+20x^29+23x^30+6x^31+8x^32+10x^33+9x^34+4x^35+3x^36+4x^37+1x^38+2x^39

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 0.00532 seconds.