The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^13+127x^14+258x^15+428x^16+694x^17+907x^18+1224x^19+1646x^20+1816x^21+1954x^22+1948x^23+1648x^24+1332x^25+994x^26+616x^27+352x^28+216x^29+111x^30+50x^31+19x^32+6x^33+3x^34+2x^36

The gray image is a code over GF(2) with n=44, k=14 and d=13.
This code was found by Heurico 1.16 in 9 seconds.