The generator matrix

 1  1  1  1  1  1  1  2  1  2  1  4  2
 0 12  0  0  0  0  0 12 12  8 12  0  8
 0  0 12  0  0  0  4  4  4  4  0  8 12
 0  0  0 12  0  4  4  0  0  4  4  4  8
 0  0  0  0 12  4  0  4 12 12 12  8  4
 0  0  0  0  0  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  8  0  0  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+34x^7+154x^8+224x^9+364x^10+982x^11+3540x^12+5700x^13+3640x^14+1006x^15+373x^16+216x^17+92x^18+26x^19+28x^20+4x^21

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 0.258 seconds.