The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  4 14 10 10  0  8  4
 0  0  2  0  6  6  6  4  8 14 12
 0  0  0  2  2  4  6  2  4 12  8

generates a code of length 11 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+40x^7+241x^8+448x^9+910x^10+4912x^11+910x^12+448x^13+241x^14+40x^15+1x^22

The gray image is a code over GF(2) with n=88, k=13 and d=28.
This code was found by Heurico 1.16 in 0.07 seconds.