The generator matrix

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

generates a code of length 17 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+249x^40+492x^41+504x^42+1008x^43+1101x^44+2088x^45+1980x^46+3504x^47+4005x^48+5568x^49+4380x^50+8400x^51+8229x^52+8280x^53+4788x^54+5520x^55+2751x^56+2004x^57+636x^58+27x^60+18x^64+3x^68

The gray image is a linear code over GF(4) with n=68, k=8 and d=40.
This code was found by Heurico 1.16 in 2.79 seconds.