The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+417x^228+828x^229+636x^230+1488x^231+2094x^232+2532x^233+1848x^234+3696x^235+4425x^236+5604x^237+3420x^238+6108x^239+7245x^240+8856x^241+5352x^242+9156x^243+10977x^244+12660x^245+7368x^246+12264x^247+12627x^248+16020x^249+8376x^250+12528x^251+13458x^252+14964x^253+7824x^254+11484x^255+11271x^256+11040x^257+5112x^258+7428x^259+6291x^260+5328x^261+2316x^262+2784x^263+2331x^264+1776x^265+624x^266+600x^267+444x^268+264x^269+132x^270+48x^271+39x^272+18x^276+12x^280+12x^284+6x^288+3x^292+6x^296+3x^300

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 355 seconds.