The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 aX aX X (a+1)X (a+1)X X aX X aX X
0 0 X 0 0 (a+1)X X 0 aX aX aX X aX 0 (a+1)X 0 (a+1)X
0 0 0 X 0 X (a+1)X (a+1)X aX 0 aX X 0 X (a+1)X X 0
0 0 0 0 X (a+1)X aX X (a+1)X X 0 X aX X aX aX 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+132x^40+150x^44+168x^48+3072x^51+186x^52+204x^56+138x^60+39x^64+6x^68
The gray image is a linear code over GF(4) with n=68, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0338 seconds.