The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  2
 0  2  0  0  0  2  0 2a  2 2a  0 2a+2  2  2
 0  0  2  0  0 2a+2  2  0 2a+2 2a+2  2 2a+2 2a+2 2a
 0  0  0  2  0  2 2a+2 2a+2 2a  0 2a 2a 2a+2 2a+2
 0  0  0  0  2 2a+2 2a  2  0 2a 2a+2 2a+2 2a 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+348x^36+1350x^40+1896x^44+276x^48+60x^52+18x^56

The gray image is a code over GF(4) with n=56, k=6 and d=32.
This code was found by Heurico 1.16 in 0.21 seconds.