The generator matrix
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 0 0
0 0 X 0 0 (a+1)X X 0 aX aX aX X aX 0 X 0
0 0 0 X 0 X (a+1)X (a+1)X aX 0 aX X 0 X 0 (a+1)X
0 0 0 0 X (a+1)X aX X (a+1)X X 0 X aX X aX (a+1)X
generates a code of length 16 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+72x^36+156x^40+174x^44+3282x^48+180x^52+168x^56+54x^60+9x^64
The gray image is a linear code over GF(4) with n=64, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0286 seconds.