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

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+684x^234+660x^235+141x^236+1608x^238+1140x^239+186x^240+1836x^242+1260x^243+258x^244+1656x^246+1176x^247+162x^248+1272x^250+840x^251+111x^252+1200x^254+360x^255+57x^256+468x^258+480x^259+63x^260+432x^262+156x^263+42x^264+60x^266+72x^267+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 1.7 seconds.