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

generates a code of length 92 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+135x^268+456x^269+348x^270+216x^271+237x^272+612x^273+276x^274+204x^275+201x^276+216x^277+84x^278+84x^279+120x^280+108x^281+132x^282+24x^283+45x^284+168x^285+60x^286+51x^288+60x^289+12x^290+12x^291+36x^292+84x^293+36x^294+36x^295+12x^297+12x^298+12x^301+3x^312+3x^332

The gray image is a linear code over GF(4) with n=368, k=6 and d=268.
This code was found by Heurico 1.16 in 0.219 seconds.