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.