The generator matrix
1 0 1 1 1 1 1 1 1 1 0 1 1 1 X (a+1)X 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a X (a+1)X+a+1 1 aX+1 X+a X+a+1 X 1 X X+1
0 0 (a+1)X X aX X 0 (a+1)X aX (a+1)X (a+1)X aX 0 X X X (a+1)X X
generates a code of length 18 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+216x^50+240x^51+24x^52+144x^54+36x^56+216x^58+144x^59+3x^64
The gray image is a linear code over GF(4) with n=72, k=5 and d=50.
This code was found by Heurico 1.16 in 3.24e-008 seconds.