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

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+264x^83+456x^84+492x^85+96x^86+912x^87+1425x^88+948x^89+192x^90+1404x^91+1563x^92+924x^93+288x^94+1644x^95+2013x^96+1020x^97+192x^98+972x^99+906x^100+456x^101+180x^103+21x^104+3x^108+12x^112

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 1.12 seconds.