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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+66x^53+139x^54+172x^55+214x^56+296x^57+384x^58+626x^59+966x^60+1670x^61+2414x^62+2576x^63+2415x^64+1714x^65+946x^66+570x^67+392x^68+232x^69+161x^70+122x^71+84x^72+110x^73+46x^74+28x^75+17x^76+8x^77+6x^78+2x^79+6x^80+1x^92

The gray image is a code over GF(2) with n=504, k=14 and d=212.
This code was found by Heurico 1.16 in 29.4 seconds.