The generator matrix

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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 249.

Homogenous weight enumerator: w(x)=1x^0+408x^249+396x^250+1728x^251+138x^252+180x^254+45x^256+180x^257+45x^260+15x^264+144x^265+180x^266+576x^267+12x^270+36x^273+9x^276+3x^280

The gray image is a linear code over GF(4) with n=340, k=6 and d=249.
This code was found by Heurico 1.16 in 6.29 seconds.