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

generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 231.

Homogenous weight enumerator: w(x)=1x^0+492x^231+888x^232+624x^233+924x^234+2148x^235+3516x^236+2424x^237+2376x^238+4380x^239+7035x^240+3948x^241+4056x^242+7764x^243+10452x^244+6204x^245+5208x^246+10812x^247+15132x^248+8136x^249+7932x^250+13212x^251+18147x^252+9396x^253+8640x^254+13896x^255+18609x^256+8592x^257+7308x^258+11568x^259+13407x^260+6276x^261+4296x^262+6528x^263+6630x^264+2568x^265+1848x^266+2328x^267+1962x^268+852x^269+408x^270+564x^271+417x^272+132x^273+12x^274+36x^275+18x^276+15x^280+15x^284+3x^288+3x^292+3x^296+3x^304

The gray image is a linear code over GF(4) with n=336, k=9 and d=231.
This code was found by Heurico 1.16 in 360 seconds.