The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^13+277x^14+490x^15+825x^16+1248x^17+1846x^18+2548x^19+3228x^20+3744x^21+3950x^22+3832x^23+3338x^24+2636x^25+1904x^26+1228x^27+748x^28+438x^29+213x^30+94x^31+52x^32+20x^33+2x^34

The gray image is a code over GF(2) with n=44, k=15 and d=13.
This code was found by Heurico 1.16 in 22.2 seconds.