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

generates a code of length 83 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 237.

Homogenous weight enumerator: w(x)=1x^0+516x^237+684x^238+324x^239+39x^240+1116x^241+1656x^242+576x^243+45x^244+1416x^245+1164x^246+384x^247+63x^248+1392x^249+1032x^250+360x^251+51x^252+900x^253+972x^254+252x^255+15x^256+792x^257+684x^258+204x^259+15x^260+492x^261+504x^262+132x^263+15x^264+204x^265+132x^266+60x^267+9x^268+84x^269+84x^270+12x^271+3x^272

The gray image is a linear code over GF(4) with n=332, k=7 and d=237.
This code was found by Heurico 1.16 in 4.21 seconds.