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

generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 246.

Homogenous weight enumerator: w(x)=1x^0+636x^246+696x^247+162x^248+1728x^250+1236x^251+183x^252+1812x^254+1260x^255+204x^256+1632x^258+936x^259+165x^260+1404x^262+780x^263+129x^264+852x^266+552x^267+99x^268+684x^270+408x^271+63x^272+360x^274+204x^275+6x^276+72x^278+72x^279+9x^280+36x^282+3x^292

The gray image is a linear code over GF(4) with n=344, k=7 and d=246.
This code was found by Heurico 1.16 in 1.38 seconds.