The generator matrix

 1  0  0  0  1  1  1  6  1  1  1
 0  1  0  0  2  5  7  1 12  9 12
 0  0  1  0  3  1  2  3 14  7  0
 0  0  0  1  1  2  3  3  4  2  6

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

Homogenous weight enumerator: w(x)=1x^0+140x^7+1129x^8+4448x^9+14742x^10+24616x^11+14742x^12+4448x^13+1129x^14+140x^15+1x^22

The gray image is a code over GF(2) with n=88, k=16 and d=28.
This code was found by Heurico 1.16 in 3.22 seconds.