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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+30x^52+102x^53+124x^54+144x^55+236x^56+584x^57+199x^58+1334x^59+534x^60+1876x^61+269x^62+1314x^63+368x^64+542x^65+116x^66+126x^67+80x^68+76x^69+44x^70+22x^71+25x^72+18x^73+13x^74+4x^75+4x^76+2x^77+3x^78+1x^80+1x^88

The gray image is a code over GF(2) with n=488, k=13 and d=208.
This code was found by Heurico 1.16 in 1.78 seconds.