The generator matrix

 1  1  1  1  2  1  1  1  2  2  2  2  2
 0  2  0  6  2  0  6  0  6  6  4 14  4
 0  0 12  0  0  0  4  4  0  8  4  8  0
 0  0  0 12  0 12  4  0  4  0  4  4  4
 0  0  0  0  4  0  0 12  4  8  4  0  8
 0  0  0  0  0  8  0  8  0  0  8  8  8
 0  0  0  0  0  0  8  8  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+36x^7+170x^8+394x^9+1468x^10+1816x^11+6516x^12+11886x^13+6616x^14+1828x^15+1477x^16+390x^17+108x^18+32x^19+28x^20+2x^21

The gray image is a code over GF(2) with n=104, k=15 and d=28.
This code was found by Heurico 1.16 in 0.724 seconds.