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  2  1  2  4  2  1  1  2  4  2  2  2  1  1  2  2  1  2  2  0  4  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4 12 12  8  4 12 12  0  8 12  4  0  8  0 12  0  4  4  4  0  4 12  0 12 12 12 12 12  0 12  0  8  4  4  0  8  0  4
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8 12  0  8  4  4  0  8  4  0  0 12  4 12 12  8  8  0  0  8 12  8  4  8  8  8  8  8  4 12 12 12  0  4  0  0  0  4
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  4  4 12  0  4  4  4  4  8  4  0  0 12  4  8  4  4  4  8 12  0  4  8  8  4  0 12 12  4 12  8  0 12 12  8  4  8
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8  0  0  0  8  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  0  0  8  8  0  8  8  0  8  8  0  0  0  8  8  8  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  8  0  8  8  8  8  8  0  0  8  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  0  0  8  8  8  0  0  8  0  0  8  8  0  8  0  8  0  8  8  0  0  0  0  8  8  8  8  8  8  8

generates a code of length 57 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+256x^48+310x^50+16x^51+765x^52+176x^53+1194x^54+512x^55+4763x^56+672x^57+4476x^58+464x^59+1421x^60+176x^61+516x^62+32x^63+357x^64+142x^66+100x^68+18x^70+15x^72+1x^76+1x^84

The gray image is a code over GF(2) with n=456, k=14 and d=192.
This code was found by Heurico 1.16 in 48 seconds.