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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+135x^56+456x^60+1024x^61+256x^62+87x^64+88x^68+1x^120

The gray image is a code over GF(2) with n=488, k=11 and d=224.
This code was found by Heurico 1.16 in 3.28 seconds.