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

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

Homogenous weight enumerator: w(x)=1x^0+199x^48+392x^50+76x^51+677x^52+252x^53+1386x^54+1500x^55+2530x^56+2508x^57+2508x^58+1444x^59+1358x^60+308x^61+580x^62+52x^63+324x^64+4x^65+164x^66+84x^68+26x^70+10x^72+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 33.8 seconds.