The generator matrix

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

generates a code of length 14 over GR(16,4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+192x^34+114x^36+576x^38+387x^40+1344x^42+468x^44+960x^46+3x^48+42x^52+9x^56

The gray image is a code over GF(4) with n=56, k=6 and d=34.
This code was found by Heurico 1.16 in 0.931 seconds.