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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+66x^54+151x^56+16x^57+201x^58+208x^59+490x^60+544x^61+775x^62+544x^63+509x^64+208x^65+166x^66+16x^67+106x^68+58x^70+15x^72+7x^74+4x^76+5x^78+3x^80+2x^82+1x^96

The gray image is a code over GF(2) with n=496, k=12 and d=216.
This code was found by Heurico 1.16 in 0.77 seconds.