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

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+1356x^239+645x^240+4332x^243+1752x^244+6324x^247+2520x^248+8424x^251+2592x^252+8592x^255+2829x^256+8232x^259+2616x^260+6372x^263+1944x^264+3816x^267+1104x^268+1452x^271+285x^272+252x^275+96x^276

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 144 seconds.