The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+30x^13+76x^14+156x^15+258x^16+356x^17+431x^18+560x^19+816x^20+932x^21+896x^22+912x^23+864x^24+632x^25+454x^26+384x^27+224x^28+94x^29+60x^30+36x^31+13x^32+4x^33+3x^34

The gray image is a code over GF(2) with n=44, k=13 and d=13.
This code was found by Heurico 1.10 in 0.559 seconds.