The generator matrix

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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 239.

Homogenous weight enumerator: w(x)=1x^0+1332x^239+729x^240+4404x^243+1551x^244+6648x^247+2484x^248+7860x^251+2796x^252+8592x^255+2649x^256+8364x^259+2838x^260+6612x^263+1980x^264+3564x^267+996x^268+1476x^271+285x^272+288x^275+75x^276+12x^279

The gray image is a linear code over GF(4) with n=340, k=8 and d=239.
This code was found by Heurico 1.16 in 64.9 seconds.