The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+38x^10+12x^11+129x^12+76x^13+308x^14+412x^15+750x^16+1372x^17+1754x^18+2712x^19+3216x^20+3608x^21+3992x^22+3608x^23+3216x^24+2712x^25+1754x^26+1372x^27+750x^28+412x^29+308x^30+76x^31+129x^32+12x^33+38x^34+1x^44

The gray image is a code over GF(2) with n=44, k=15 and d=10.
This code was found by Heurico 1.16 in 6.27 seconds.