The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+288x^31+174x^32+108x^33+912x^34+1596x^35+1443x^36+1068x^37+3168x^38+5532x^39+5691x^40+3300x^41+9360x^42+11796x^43+8202x^44+3204x^45+4992x^46+3828x^47+837x^48+27x^52+9x^56

The gray image is a code over GF(4) with n=56, k=8 and d=31.
This code was found by Heurico 1.16 in 2.22 seconds.