The generator matrix

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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 234.

Homogenous weight enumerator: w(x)=1x^0+564x^234+480x^235+402x^236+300x^237+1344x^238+936x^239+507x^240+312x^241+1464x^242+924x^243+516x^244+336x^245+1512x^246+804x^247+414x^248+204x^249+1104x^250+528x^251+279x^252+180x^253+756x^254+432x^255+222x^256+120x^257+588x^258+348x^259+105x^260+48x^261+276x^262+132x^263+96x^264+36x^265+72x^266+24x^267+15x^268+3x^276

The gray image is a linear code over GF(4) with n=328, k=7 and d=234.
This code was found by Heurico 1.16 in 2.21 seconds.