The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 aX 1 X 1 1 1 aX
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 (a+1)X+a+1 X+a 1 X (a+1)X+1 aX+a+1 X+a X 1 aX+a+1 1 X aX+1 a+1 X+a 1 0 X a aX+1 (a+1)X+a+1 1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X 0 (a+1)X aX aX 0 (a+1)X aX (a+1)X aX aX (a+1)X X X 0 X (a+1)X X X X aX (a+1)X 0
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX aX (a+1)X 0 X 0 aX (a+1)X X 0 aX 0 0 aX (a+1)X X aX (a+1)X aX aX X 0 aX
generates a code of length 36 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.
Homogenous weight enumerator: w(x)=1x^0+492x^100+1161x^104+858x^108+1059x^112+504x^116+3x^120+6x^124+12x^132
The gray image is a linear code over GF(4) with n=144, k=6 and d=100.
This code was found by Heurico 1.16 in 0.0494 seconds.