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.