The generator matrix

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

generates a code of length 83 over F4[X]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+393x^228+636x^229+732x^230+1092x^231+2154x^232+2676x^233+3144x^234+2460x^235+4593x^236+5160x^237+5520x^238+4500x^239+6918x^240+9156x^241+8664x^242+6468x^243+10125x^244+11304x^245+11208x^246+8760x^247+13605x^248+13356x^249+12972x^250+10200x^251+13929x^252+13644x^253+12072x^254+8280x^255+10974x^256+10344x^257+8688x^258+5076x^259+6285x^260+5460x^261+3468x^262+1812x^263+2172x^264+1704x^265+996x^266+468x^267+444x^268+276x^269+120x^270+36x^271+24x^272+12x^273+27x^276+21x^280+6x^284+3x^288+3x^292+3x^308

The gray image is a linear code over GF(4) with n=332, k=9 and d=228.
This code was found by Heurico 1.16 in 374 seconds.