The generator matrix

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

generates a code of length 10 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+42x^6+32x^7+63x^8+224x^9+1324x^10+224x^11+63x^12+32x^13+42x^14+1x^20

The gray image is a code over GF(2) with n=80, k=11 and d=24.
This code was found by Heurico 1.16 in 0.00457 seconds.