The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^12+108x^14+282x^16+360x^18+716x^20+1064x^22+712x^24+480x^26+276x^28+12x^30+29x^32+24x^34+4x^36

The gray image is a code over GF(2) with n=44, k=12 and d=12.
This code was found by Heurico 1.16 in 0.256 seconds.