The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^7+411x^8+1306x^9+3264x^10+6084x^11+3391x^12+1316x^13+336x^14+122x^15+20x^16+2x^17+1x^20

The gray image is a code over GF(2) with n=88, k=14 and d=28.
This code was found by Heurico 1.16 in 28.8 seconds.