The generator matrix

 1  0  0  1  1  1  1  1 a^2*X  1  1  1  1  X  1  1  1
 0  1  0 a^2*X a*X  X  1 a^2*X+1  1 a*X+1 a^2*X+a  a a*X+a  1 X+a^2 a^2*X+a^2 a*X+a^2
 0  0  1  1  a a^2 X+a^2 a*X+a  1 a^2*X+1 a*X a^2*X+a^2 X+a a*X+a^2 a^2*X+a X+1  X

generates a code of length 17 over F4[X]/(X^2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+1152x^47+540x^48+768x^51+192x^52+1152x^55+288x^56+3x^64

The gray image is a linear code over GF(4) with n=68, k=6 and d=47.
This code was found by Heurico 1.16 in 2.53 seconds.