The generator matrix
1 1 1 1 2 2 1
0 2 0 2 4 12 6
0 0 2 2 2 2 0
0 0 0 4 0 12 8
generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+60x^4+256x^5+696x^6+2056x^7+729x^8+240x^9+48x^10+8x^11+2x^12
The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00616 seconds.