The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  0  X  1 a^2*X a*X  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1 a*X  1  1  1  X  0 a*X  1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1 a*X  1  1  1 a^2*X  1  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a*X+a^2 a^2 a^2*X+1  1  1 a*X  1  1 a*X+a  1  X X+a^2 a*X X+1 a*X a^2*X+1 a^2*X+a^2 a^2*X+1  1  0  a  a a*X+a^2  1 a*X+a^2  a  0  1  1  1 a^2*X+1  1 a*X a*X+1 X+a X+a^2  a a*X+a^2 a^2  a a^2*X+a  X a^2*X  0 X+a^2 X+1 a^2  1 a*X+a^2  X a*X+1 a*X+a X+a a*X+a^2  a a^2*X  1 X+1 a^2*X a^2*X+a X+a  1  0  a a^2*X+1  X a*X+a a*X+1
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a^2*X+a a^2  0 X+a  0 a*X a^2*X+1 X+a^2 a^2 a*X+a X+1 a^2*X+1  1 a*X+1  a a^2  X X+1 a^2*X X+1 a*X a*X+1 a*X a^2 a*X+1 a^2*X+1 a*X+a^2 X+a^2 a*X+1 a*X+a^2 a^2*X+a^2 a^2*X+a  1  X a^2*X  a a*X+a X+1 X+1 a^2 X+a  a  X a*X X+a^2 a^2*X+a X+a^2  a  X a^2 a^2*X+a a*X a^2*X X+1 a^2*X  a X+a X+1 X+a a^2*X+a X+a  X  1 a*X+a^2 a*X+a  1 a*X+1 a^2*X+a^2
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2 a^2*X+1  0 a*X a^2*X a^2*X+a^2 a^2*X+a^2 a^2*X+a^2  0 a^2*X+1 X+a^2 X+a  1 X+1  1 a*X+1 X+a a*X+a a^2*X+a X+1  X a^2*X+a  1  0  a X+a a^2*X+a a*X+a^2 X+1 X+1 X+a^2  X  1 a*X+a^2  X a^2*X+a^2 X+a^2 a*X+a a^2*X+a a*X a*X+a^2  1 X+a^2 a*X+1  a a*X+a a^2*X+1  1 a^2*X+a a^2 a^2 X+1 X+1 a^2*X a^2*X+a^2 a^2*X+a  a  X  a  0 a^2*X a^2*X X+a a*X+a^2  1  0 a^2*X+a a*X+a a^2*X+a^2
 0  0  0  0  X  0 a*X  0  0  0  X  X a*X a*X  X  X a*X a*X a^2*X a^2*X  X  0 a^2*X  X  X a*X a^2*X a*X a*X  X  X a*X  0  0 a^2*X  X  0 a*X  X a*X  X  X  0  0 a*X a*X  0 a^2*X a*X a*X  X a^2*X  X  0  0  X  X  0  0 a*X  0 a^2*X a^2*X a*X  X  X  X  X a^2*X a^2*X  X  0 a*X a^2*X  0 a*X a*X  X a^2*X  X

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

Homogenous weight enumerator: w(x)=1x^0+336x^219+321x^220+792x^221+1068x^222+2304x^223+2127x^224+2484x^225+2976x^226+5340x^227+3888x^228+4884x^229+5976x^230+8604x^231+6003x^232+7872x^233+8496x^234+12468x^235+8115x^236+10440x^237+10968x^238+16092x^239+9978x^240+12192x^241+12360x^242+17316x^243+10170x^244+10992x^245+10128x^246+13308x^247+7809x^248+7872x^249+6624x^250+7308x^251+3612x^252+3120x^253+2364x^254+2484x^255+1017x^256+684x^257+456x^258+432x^259+108x^260+108x^261+24x^262+24x^263+39x^264+24x^268+15x^272+12x^276+3x^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 350 seconds.