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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+84x^51+173x^52+216x^53+341x^54+416x^55+504x^56+716x^57+1549x^58+1060x^59+5705x^60+1642x^61+8077x^62+1490x^63+5704x^64+1286x^65+1497x^66+600x^67+558x^68+342x^69+254x^70+212x^71+131x^72+78x^73+54x^74+40x^75+23x^76+8x^77+4x^78+2x^79+1x^92

The gray image is a code over GF(2) with n=496, k=15 and d=204.
This code was found by Heurico 1.16 in 30.3 seconds.