The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  1  6  1  1 10  1  1 12  1  1  1  1  0  6  1  1  1  1  1  1  1  1  1  1  1  1 12 10  0  8  6 14  1  1  1  1 12  2  4  2  1
 0  1  3  6  5  1 15 12  1 10  9  1  0  3  1  6  5  1 12 15  1 10  9  1  0  6  3  9  1  1 10 12  6 10  0  8 15  5  3  5 11 13  1  1  1  1  1  1 14  2 12  4  2 14  2  2  0
 0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  8  8  8  0  0  0  8  8  0  0  0  8  0  8  8  8  8  0  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  8  8  8
 0  0  0  8  0  8  8  8  8  0  8  0  0  0  8  0  0  8  8  8  0  8  8  0  8  0  8  0  8  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  8  0  0  0  8  8  8  8  0  0
 0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  0  0  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  0  8  8  0  8  8  8  0  0  0  8  0  0  8  8

generates a code of length 57 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+108x^53+238x^54+288x^55+290x^56+280x^57+250x^58+224x^59+220x^60+108x^61+22x^62+1x^64+16x^65+2x^74

The gray image is a code over GF(2) with n=456, k=11 and d=212.
This code was found by Heurico 1.16 in 0.124 seconds.