The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+396x^225+636x^226+840x^227+780x^228+2208x^229+3000x^230+2484x^231+1602x^232+5628x^233+5628x^234+4248x^235+3633x^236+9684x^237+9180x^238+7056x^239+4614x^240+13836x^241+12288x^242+8844x^243+6246x^244+17064x^245+15060x^246+11112x^247+6639x^248+17952x^249+15360x^250+10176x^251+5868x^252+13980x^253+11196x^254+6720x^255+3549x^256+8064x^257+5412x^258+2964x^259+1485x^260+2928x^261+1860x^262+756x^263+270x^264+396x^265+228x^266+96x^267+60x^268+24x^269+24x^270+27x^272+9x^276+15x^280+6x^284+3x^288+6x^292+3x^300

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 383 seconds.