The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+81x^12+84x^13+202x^14+448x^15+890x^16+1148x^17+1690x^18+2688x^19+3405x^20+3976x^21+3940x^22+3584x^23+3056x^24+2616x^25+2132x^26+1408x^27+699x^28+356x^29+210x^30+64x^31+53x^32+12x^33+18x^34+7x^36

The gray image is a code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.16 in 10.6 seconds.