The generator matrix

 1  1  1  1  1  1  1  2  1  2  2  1  1
 0 12  0  0  0  0  8 12  4  4  8 12  8
 0  0 12  0  0  0 12  4 12  8  0  8  8
 0  0  0 12  0  0  4  0  8 12  4 12 12
 0  0  0  0 12  0  4  8 12  4  0  4  0
 0  0  0  0  0 12  4  4  0  4  8  8  0

generates a code of length 13 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+50x^7+132x^8+190x^9+350x^10+842x^11+1578x^12+10118x^13+1510x^14+854x^15+443x^16+186x^17+58x^18+46x^19+22x^20+2x^21+2x^22

The gray image is a code over GF(2) with n=104, k=14 and d=28.
This code was found by Heurico 1.16 in 0.301 seconds.