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

generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 222.

Homogenous weight enumerator: w(x)=1x^0+372x^222+480x^223+690x^224+960x^225+2568x^226+2556x^227+2250x^228+2580x^229+5340x^230+5124x^231+3888x^232+4284x^233+9324x^234+8748x^235+6072x^236+7092x^237+13488x^238+11508x^239+7515x^240+8628x^241+17904x^242+13824x^243+8856x^244+9636x^245+17388x^246+14280x^247+8322x^248+8604x^249+15060x^250+10728x^251+5997x^252+5004x^253+7620x^254+4836x^255+2694x^256+1884x^257+2544x^258+1476x^259+615x^260+456x^261+528x^262+156x^263+120x^264+24x^265+24x^266+12x^267+39x^268+18x^272+18x^276+6x^284+3x^292

The gray image is a linear code over GF(4) with n=324, k=9 and d=222.
This code was found by Heurico 1.16 in 339 seconds.