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

generates a code of length 92 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+1281x^264+2952x^268+3330x^272+2844x^276+2472x^280+1416x^284+1047x^288+588x^292+375x^296+72x^300+6x^304

The gray image is a linear code over GF(4) with n=368, k=7 and d=264.
This code was found by Heurico 1.16 in 10.7 seconds.