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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+116x^54+196x^56+423x^58+256x^59+852x^60+512x^61+808x^62+256x^63+395x^64+125x^66+83x^68+50x^70+8x^72+11x^74+2x^78+1x^82+1x^100

The gray image is a code over GF(2) with n=488, k=12 and d=216.
This code was found by Heurico 1.16 in 1.91 seconds.