The generator matrix

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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+348x^225+696x^226+1080x^227+1131x^228+1632x^229+2364x^230+3228x^231+2916x^232+4476x^233+4380x^234+5784x^235+4992x^236+7536x^237+6708x^238+8904x^239+7236x^240+11232x^241+9336x^242+12684x^243+9372x^244+13908x^245+11904x^246+14256x^247+10011x^248+14316x^249+11568x^250+13860x^251+9273x^252+11664x^253+8268x^254+9060x^255+5484x^256+6108x^257+4416x^258+3852x^259+2319x^260+2100x^261+1548x^262+924x^263+357x^264+384x^265+228x^266+84x^267+96x^268+24x^269+24x^270+12x^271+12x^272+21x^276+6x^280+9x^284+9x^288+3x^292

The gray image is a linear code over GF(4) with n=328, k=9 and d=225.
This code was found by Heurico 1.16 in 349 seconds.