The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+64x^15+148x^16+188x^17+256x^18+336x^19+373x^20+414x^21+454x^22+460x^23+440x^24+370x^25+260x^26+152x^27+91x^28+50x^29+22x^30+12x^31+2x^32+2x^33+1x^40

The gray image is a code over GF(2) with n=44, k=12 and d=15.
This code was found by Heurico 1.16 in 93.2 seconds.