The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  0  1  1  1  X  1  1  1  1  1  1 aX  1  1  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  0  1 (a+1)X+a+1 (a+1)X+1  a  1 (a+1)X+a+1  X  X aX+a+1 X+a  a  1 X+a a+1  0
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X (a+1)X  0  0 aX (a+1)X (a+1)X (a+1)X  0 (a+1)X  X aX  X aX (a+1)X (a+1)X aX  0  X
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  0 aX  X  X aX (a+1)X (a+1)X (a+1)X  0  X  X aX (a+1)X  X  X (a+1)X (a+1)X (a+1)X
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX  0 aX aX  X  0  X  X (a+1)X (a+1)X aX  0 aX (a+1)X  X  0 (a+1)X  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+159x^80+12x^81+144x^83+873x^84+144x^85+384x^87+1647x^88+648x^89+864x^91+3012x^92+1296x^93+1152x^95+3036x^96+972x^97+528x^99+1308x^100+81x^104+72x^108+36x^112+15x^116

The gray image is a linear code over GF(4) with n=124, k=7 and d=80.
This code was found by Heurico 1.16 in 0.605 seconds.