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 12  2  1  2  1 12  1  1  2  1  2  8  1  1  1  1  4  1  2  1  4  1  1  4  1  0  2  1  1  2  0 12  1  2 12  1  1  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  4 14  2  0 10  8 10 10  4 14  2  2  6  6 12  8  2  4 14  4 12  2  8 14  8 12  2  4  2  2  8  6  2  4  0  2 14  6 10 12  2  2 14 12  2  6  0  0
 0  0  2  2 12  6  6  4  4  2  6  0  0 14  2 12  8  6 10  0  2  8  0 14 10  2  0 14  2  4 10 12 12 10 12  8  6 10 12  2  6 10 14  2  0  4  2  4  6  2  8  8 10  6  8 10 10  2 10  4  0
 0  0  0  8  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  0  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0
 0  0  0  0  8  0  8  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0  0  8  0  8  0  0  8  8  8  8  8  0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  0  8  0  8  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0  8  8  8  8  8  0  8  0  0  8  0  0  0  0  0  0  8  0  8  8  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^54+168x^55+266x^56+586x^57+679x^58+810x^59+1010x^60+1364x^61+894x^62+780x^63+609x^64+408x^65+200x^66+124x^67+86x^68+60x^69+32x^70+36x^71+12x^72+14x^73+1x^74+2x^75+1x^86

The gray image is a code over GF(2) with n=488, k=13 and d=216.
This code was found by Heurico 1.16 in 1.23 seconds.