The generator matrix

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

generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+288x^80+300x^81+468x^82+876x^83+1875x^84+1764x^85+1380x^86+2268x^87+3711x^88+3168x^89+2808x^90+3120x^91+6246x^92+5328x^93+4248x^94+4560x^95+7164x^96+5076x^97+2868x^98+2628x^99+2931x^100+1260x^101+516x^102+372x^103+297x^104+12x^108+3x^112

The gray image is a linear code over GF(4) with n=124, k=8 and d=80.
This code was found by Heurico 1.16 in 7.85 seconds.