The generator matrix

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

generates a code of length 80 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 222.

Homogenous weight enumerator: w(x)=1x^0+168x^222+420x^223+366x^224+360x^225+1488x^226+1152x^227+906x^228+444x^229+3336x^230+2064x^231+1353x^232+732x^233+4308x^234+2856x^235+1680x^236+1164x^237+5976x^238+3504x^239+1788x^240+1248x^241+5688x^242+3096x^243+1665x^244+1044x^245+5172x^246+3096x^247+1344x^248+732x^249+3108x^250+1656x^251+645x^252+324x^253+1272x^254+492x^255+354x^256+96x^257+192x^258+72x^259+57x^260+12x^262+24x^263+21x^264+21x^268+12x^272+12x^276+6x^280+6x^284+3x^288

The gray image is a linear code over GF(4) with n=320, k=8 and d=222.
This code was found by Heurico 1.16 in 24 seconds.