The generator matrix

 1  0  1  1  1  1  1  1  0  1  1  0  1  1  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1  a  1  0 (a+1)X+1  1 (a+1)X+a+1  a (a+1)X+1 (a+1)X+1  a  0
 0  0 (a+1)X  0  0  X  0  X  X  X (a+1)X aX (a+1)X aX  X  0  0  0
 0  0  0  X  0 (a+1)X (a+1)X (a+1)X  X aX (a+1)X  0 aX  0  X  0 (a+1)X  0
 0  0  0  0 (a+1)X  X (a+1)X aX (a+1)X (a+1)X (a+1)X  X (a+1)X  X  X  X (a+1)X  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+48x^40+60x^42+48x^43+144x^44+48x^45+432x^46+288x^47+333x^48+432x^49+1224x^50+768x^51+1317x^52+1296x^53+2160x^54+1248x^55+1896x^56+1296x^57+2268x^58+720x^59+186x^60+132x^64+33x^68+6x^72

The gray image is a linear code over GF(4) with n=72, k=7 and d=40.
This code was found by Heurico 1.16 in 0.262 seconds.