The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^13+104x^14+56x^15+234x^16+384x^17+560x^18+576x^19+192x^20+1008x^21+1712x^22+1008x^23+488x^24+576x^25+640x^26+384x^27+64x^28+56x^29+40x^30+24x^31+45x^32+16x^34

The gray image is a code over GF(2) with n=44, k=13 and d=13.
This code was found by Heurico 1.16 in 24.7 seconds.