The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+32x^57+17x^58+8x^59+3x^60+3x^62

The gray image is a code over GF(2) with n=456, k=6 and d=228.
This code was found by Heurico 1.16 in 0.0728 seconds.