The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+246x^14+947x^16+1723x^18+3189x^20+4008x^22+3426x^24+1834x^26+714x^28+250x^30+42x^32+3x^34+1x^36

The gray image is a code over GF(2) with n=44, k=14 and d=14.
This code was found by Heurico 1.16 in 10.9 seconds.