The generator matrix

 1  0  0  1  1  1  1  1  1  1  X  1  1  1  1  1 aX
 0  1  0 (a+1)X  X aX  1 (a+1)X+1 aX+a+1 (a+1)X+a+1  1 X+1 X+a (a+1)X+a aX+a X+a+1  1
 0  0  1  1 (a+1)X+a (a+1)X+a+1 a+1 X+a aX+1  X X+a+1 (a+1)X+1 (a+1)X  a aX+a+1 aX+a  1

generates a code of length 17 over F4[X,sigma]/(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 0.828 seconds.