The generator matrix

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

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+408x^80+624x^81+180x^82+768x^83+2001x^84+2052x^85+432x^86+1680x^87+4131x^88+4176x^89+504x^90+4752x^91+7530x^92+6552x^93+1008x^94+5424x^95+7767x^96+6048x^97+756x^98+2736x^99+3450x^100+2052x^101+192x^102+198x^104+66x^108+36x^112+9x^116+3x^120

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 37 seconds.