The generator matrix

 1  1  1  1  1  1  1  1  1  2  2
 0 12  0  0  0  4 12 12  8  8  0
 0  0 12  0  4  4  4  0  8  0  4
 0  0  0 12  4  8  4  4 12  4 12
 0  0  0  0  8  8  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+24x^7+60x^8+96x^9+202x^10+1296x^11+188x^12+96x^13+52x^14+24x^15+7x^16+2x^18

The gray image is a code over GF(2) with n=88, k=11 and d=28.
This code was found by Heurico 1.16 in 0.00644 seconds.