The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  1  1  1  1  1  1  1
 0  2  0  6  8  6  0 10  4  6 12  2  4  2  4 14  0 14  2  4 12 10 12 10  8 10  4 10  8  2  8  6  0  4  6  0  2  6  0  2 10  0 14 12 12 12  2 14 14  8  2 14 14  8  0  0 12
 0  0 12  0  0  4  4 12  4  8 12  8  0  4  0 12 12  4  8  8  8  0 12 12 12  0  0  4  8  4  4  0  8  4  8  0  4 12  4  0 12  8  4  8  4 12 12  4  8  0  8  0  8  0  4 12  0
 0  0  0 12  4 12  4  0  0  0  4 12  4  4  0  8 12  8  0  8 12 12  8  4  4  4  8 12 12  0  8  0  0 12 12 12  8  4  0  8  8  8  4  4  8 12 12  0  8  0  4  8  4  8 12  8 12

generates a code of length 57 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+96x^53+112x^54+128x^55+798x^56+32x^57+624x^58+32x^59+128x^61+96x^63+1x^112

The gray image is a code over GF(2) with n=456, k=11 and d=212.
This code was found by Heurico 1.16 in 23.3 seconds.