The generator matrix

 1  0  1  1  1 12  1  2  1  1
 0  1  1 12 11  1  6  2  7  4
 0  0  2  6  4  6  0  2  4 12
 0  0  0  8  0  0  8  8  8  8

generates a code of length 10 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+50x^7+378x^8+720x^9+1812x^10+716x^11+356x^12+48x^13+12x^14+2x^15+1x^16

The gray image is a code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.0138 seconds.