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.