The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+32x^22+78x^23+88x^24+112x^25+93x^26+82x^27+97x^28+74x^29+94x^30+90x^31+57x^32+44x^33+33x^34+22x^35+13x^36+10x^37+4x^38

The gray image is a code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.10 in 0.016 seconds.