The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  2  1  1  1  1  2  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
 0  1  1  a a+1  0 2a+3 a+1  a  1 a+3  2 2a+3 a+2  1  2  1 a+2 a+3  1  0  2 2a+3 2a+1 2a+1 a+2 3a 3a 2a 2a 2a+1  a a+1 a+3 3a+1 3a+1 2a  1 3a 3a+1 2a  0  2 2a+1  1 2a+3  a a+2 3a a+1 a+3 3a+1 2a+2 2a+2 2a+2  3
 0  0 2a+2 2a  2  2  0 2a+2  0 2a 2a 2a+2 2a  2  2 2a  2 2a+2  0 2a+2 2a  2  2 2a+2  0 2a  0  2 2a+2  0 2a 2a+2  0 2a+2  2 2a  2  0 2a  0 2a 2a+2  0  2 2a 2a+2  2  0 2a+2 2a  2 2a+2 2a+2 2a  2  0

generates a code of length 56 over GR(16,4) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+156x^164+72x^165+144x^167+366x^168+108x^169+48x^171+84x^172+6x^176+12x^177+24x^180+3x^208

The gray image is a code over GF(4) with n=224, k=5 and d=164.
This code was found by Heurico 1.16 in 0.032 seconds.