The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+396x^32+456x^33+624x^34+984x^35+2310x^36+2088x^37+2160x^38+3000x^39+7890x^40+8280x^41+4560x^42+6408x^43+11808x^44+7608x^45+3408x^46+1896x^47+1641x^48+18x^52

The gray image is a code over GF(4) with n=56, k=8 and d=32.
This code was found by Heurico 1.16 in 85.7 seconds.