The generator matrix

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

generates a code of length 80 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 219.

Homogenous weight enumerator: w(x)=1x^0+300x^219+735x^220+432x^221+948x^222+2268x^223+3201x^224+1284x^225+2016x^226+5640x^227+6708x^228+2748x^229+4560x^230+9576x^231+10023x^232+3216x^233+7152x^234+13668x^235+13965x^236+5244x^237+8976x^238+17568x^239+17400x^240+6456x^241+10032x^242+17592x^243+16794x^244+5532x^245+8364x^246+14472x^247+12846x^248+3936x^249+4800x^250+7992x^251+6195x^252+1380x^253+2004x^254+2628x^255+1821x^256+468x^257+288x^258+408x^259+345x^260+24x^261+12x^262+48x^263+27x^264+21x^268+3x^272+15x^276+6x^280+6x^284

The gray image is a linear code over GF(4) with n=320, k=9 and d=219.
This code was found by Heurico 1.16 in 337 seconds.