The generator matrix
1 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 (a+1)X 0 0
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 0 X 0 X (a+1)X (a+1)X aX 0 aX X 0 X aX X aX 0
0 0 0 0 X (a+1)X aX X (a+1)X X 0 X aX X aX (a+1)X aX 0
generates a code of length 18 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+54x^40+120x^44+156x^48+180x^52+3072x^54+180x^56+144x^60+147x^64+36x^68+6x^72
The gray image is a linear code over GF(4) with n=72, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0341 seconds.