The generator matrix

 1  0  1  1  1  4  2  1  1  1  1
 0  1  1  0 11  1  2  3 10  2 12
 0  0  2  6  4  6  2  4  6 14  4
 0  0  0 12  0  4  8  4  0  4 12
 0  0  0  0  8  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+68x^7+311x^8+1296x^9+3120x^10+6744x^11+3207x^12+1296x^13+256x^14+68x^15+16x^16+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 0.192 seconds.