The generator matrix

 1  0  0  1  1  1 (a+1)X  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  a a+1  1 (a+1)X (a+1)X+1 X+1 (a+1)X  1  0 X+a+1 a+1 aX+a+1 (a+1)X+1  0
 0  0  1 a+1  a  1  1  1  0 (a+1)X+1 aX+1 (a+1)X X+a+1  X X+a+1 aX+a a+1  X
 0  0  0  X  0  X aX (a+1)X (a+1)X  X  0 aX aX aX  0  X aX  0

generates a code of length 18 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+159x^44+72x^45+48x^46+504x^47+963x^48+744x^49+144x^50+840x^51+1785x^52+2328x^53+336x^54+1608x^55+2550x^56+2232x^57+240x^58+888x^59+897x^60+30x^64+15x^68

The gray image is a linear code over GF(4) with n=72, k=7 and d=44.
This code was found by Heurico 1.16 in 0.184 seconds.