The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+48x^36+432x^37+144x^38+480x^39+222x^40+864x^41+96x^42+360x^44+1008x^45+144x^46+288x^47+9x^48

The gray image is a code over GF(4) with n=56, k=6 and d=36.
This code was found by Heurico 1.16 in 0.015 seconds.