The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1 (a+1)X (a+1)X  1  1  1  1  1  1  1  1  1 (a+1)X  X
 0  1  0  0  X (a+1)X  1 (a+1)X+a a+1 (a+1)X+1 aX+1  1  1 aX+a a+1  a (a+1)X+a+1  a  1  1 (a+1)X+a+1 (a+1)X aX+a aX+1 aX+a+1 (a+1)X+1 a+1 aX+1 X+a+1  1  1
 0  0  1  1 (a+1)X+a a+1 a+1 X+a+1 X+a+1  a (a+1)X  1 X+a (a+1)X+1 X+1  0 aX X+a (a+1)X+a+1 aX+1  a (a+1)X+1 (a+1)X aX+1 X+a X+a X+1  a (a+1)X+a+1 aX+a X+a
 0  0  0 (a+1)X  X  0 aX aX (a+1)X  X  X  0 (a+1)X aX aX  X aX  0 aX (a+1)X  0  X  0 aX aX  0  X aX  0  X aX

generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+288x^83+315x^84+588x^85+1416x^87+834x^88+1068x^89+1968x^91+1179x^92+1332x^93+2304x^95+1083x^96+996x^97+1584x^99+645x^100+624x^101+120x^103+18x^104+21x^108

The gray image is a linear code over GF(4) with n=124, k=7 and d=83.
This code was found by Heurico 1.16 in 2.06 seconds.