The generator matrix

1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 2 1 1 1 1
0 1 0 0 0 0 0 0 1 2 3 1 0 3 2 3 0 2 0 0 0 0
0 0 1 0 0 0 0 1 0 2 1 1 3 0 2 2 1 1 1 0 0 0
0 0 0 1 0 0 0 1 1 3 2 0 3 0 0 1 2 2 1 1 0 0
0 0 0 0 1 0 0 1 2 1 2 3 2 3 0 0 3 0 3 1 0 0
0 0 0 0 0 1 0 1 3 0 3 2 2 0 3 2 1 0 0 0 0 0
0 0 0 0 0 0 1 2 1 3 0 3 2 2 1 0 1 3 3 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+94x^12+378x^14+1054x^16+1934x^18+2979x^20+3458x^22+3038x^24+1946x^26+1066x^28+332x^30+83x^32+16x^34+5x^36

The gray image is a code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.10 in 1.8 seconds.