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

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

Homogenous weight enumerator: w(x)=1x^0+94x^54+8x^55+203x^56+40x^57+260x^58+320x^59+781x^60+800x^61+754x^62+312x^63+200x^64+56x^65+112x^66+66x^68+52x^70+28x^72+8x^74+1x^100

The gray image is a code over GF(2) with n=488, k=12 and d=216.
This code was found by Heurico 1.16 in 0.63 seconds.