The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+147x^32+192x^33+348x^36+1728x^37+1350x^40+5184x^41+1896x^44+5184x^45+276x^48+60x^52+18x^56

The gray image is a code over GF(4) with n=56, k=7 and d=32.
This code was found by Heurico 1.16 in 2.31 seconds.