The generator matrix

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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+240x^232+516x^233+276x^234+684x^235+1770x^236+1764x^237+1188x^238+1344x^239+3006x^240+2544x^241+1500x^242+1968x^243+4062x^244+2724x^245+2112x^246+2196x^247+4167x^248+3288x^249+1740x^250+2160x^251+3978x^252+3024x^253+1824x^254+1884x^255+3549x^256+2352x^257+1296x^258+1416x^259+2130x^260+1572x^261+636x^262+516x^263+867x^264+516x^265+132x^266+108x^267+276x^268+132x^269+48x^270+12x^271+18x^272

The gray image is a linear code over GF(4) with n=332, k=8 and d=232.
This code was found by Heurico 1.16 in 26.2 seconds.