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

generates a code of length 58 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+32x^49+95x^50+90x^51+175x^52+172x^53+273x^54+436x^55+863x^56+1318x^57+1328x^58+1326x^59+859x^60+446x^61+277x^62+162x^63+107x^64+66x^65+51x^66+32x^67+35x^68+14x^69+17x^70+2x^71+5x^72+5x^74+3x^76+1x^78+1x^90

The gray image is a code over GF(2) with n=464, k=13 and d=196.
This code was found by Heurico 1.16 in 6.68 seconds.