The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+7x^54+106x^55+7x^56+1x^62+6x^63

The gray image is a code over GF(2) with n=440, k=7 and d=216.
This code was found by Heurico 1.16 in 0.0759 seconds.