The generator matrix

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

generates a code of length 80 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+339x^232+276x^233+240x^234+168x^235+543x^236+324x^237+276x^238+96x^239+345x^240+264x^241+72x^242+36x^243+186x^244+96x^245+96x^246+48x^247+225x^248+120x^249+24x^250+24x^251+48x^252+48x^253+24x^254+39x^256+12x^257+24x^258+12x^259+60x^260+12x^261+12x^262+3x^268+3x^272

The gray image is a linear code over GF(4) with n=320, k=6 and d=232.
This code was found by Heurico 1.16 in 0.157 seconds.