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.