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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+78x^55+49x^56+78x^58+142x^59+112x^60+128x^61+1292x^62+352x^63+1324x^64+128x^65+144x^66+96x^67+16x^68+4x^70+98x^71+31x^72+18x^74+2x^75+2x^80+1x^112

The gray image is a code over GF(2) with n=504, k=12 and d=220.
This code was found by Heurico 1.16 in 64.8 seconds.