The generator matrix

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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 231.

Homogenous weight enumerator: w(x)=1x^0+216x^231+360x^232+276x^233+612x^234+1560x^235+915x^236+744x^237+1380x^238+2820x^239+1851x^240+1224x^241+1956x^242+4164x^243+1857x^244+1464x^245+2808x^246+5184x^247+2334x^248+1680x^249+2832x^250+4848x^251+2124x^252+1572x^253+3024x^254+4164x^255+1917x^256+1368x^257+1908x^258+3156x^259+1194x^260+672x^261+744x^262+1200x^263+501x^264+156x^265+84x^266+288x^267+147x^268+60x^269+12x^270+48x^271+33x^272+36x^276+12x^280+12x^284+9x^288+3x^292+3x^296+3x^304

The gray image is a linear code over GF(4) with n=332, k=8 and d=231.
This code was found by Heurico 1.16 in 26.9 seconds.