The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+36x^23+120x^24+200x^25+172x^26+84x^27+24x^28+24x^30+60x^31+111x^32+120x^33+60x^34+12x^35

The gray image is a code over GF(2) with n=56, k=10 and d=23.
This code was found by Heurico 1.16 in 10.5 seconds.