The generator matrix

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

generates a code of length 91 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+288x^265+372x^266+144x^267+186x^268+540x^269+444x^270+276x^271+126x^272+408x^273+204x^274+48x^275+33x^276+216x^277+72x^278+24x^279+45x^280+48x^281+84x^282+36x^283+30x^284+144x^285+96x^286+24x^287+48x^289+36x^290+12x^291+24x^292+36x^293+36x^294+12x^295+3x^316

The gray image is a linear code over GF(4) with n=364, k=6 and d=265.
This code was found by Heurico 1.16 in 0.218 seconds.