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 1 1 1 1 1 1 X
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 (a+1)X+a aX 1 X+a+1 X+1 X X+a+1 1 aX+a+1 (a+1)X
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 X X (a+1)X X aX aX aX
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 X (a+1)X X (a+1)X 0 aX aX
generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+138x^84+192x^85+108x^86+408x^88+396x^89+156x^90+432x^92+348x^93+324x^94+543x^96+420x^97+180x^98+237x^100+180x^101+15x^104+6x^108+6x^112+3x^116+3x^120
The gray image is a linear code over GF(4) with n=124, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0409 seconds.