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

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

Homogenous weight enumerator: w(x)=1x^0+35x^52+78x^53+102x^54+158x^55+233x^56+286x^57+551x^58+872x^59+1171x^60+1358x^61+1157x^62+870x^63+499x^64+254x^65+168x^66+106x^67+79x^68+60x^69+60x^70+36x^71+27x^72+12x^73+9x^74+6x^75+3x^76+1x^94

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 1.71 seconds.