The generator matrix

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

generates a code of length 15 over GR(16,4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+333x^40+576x^41+408x^42+672x^44+384x^45+144x^46+783x^48+576x^49+216x^50+3x^56

The gray image is a code over GF(4) with n=60, k=6 and d=40.
This code was found by Heurico 1.16 in 6.87e-008 seconds.