The generator matrix

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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+75x^236+204x^237+72x^238+444x^239+1068x^240+1344x^241+144x^242+1296x^243+2676x^244+2100x^245+360x^246+1824x^247+3591x^248+3276x^249+492x^250+2640x^251+4245x^252+3888x^253+636x^254+2712x^255+4356x^256+3684x^257+564x^258+2892x^259+4560x^260+3480x^261+432x^262+2112x^263+2961x^264+2100x^265+228x^266+1032x^267+1401x^268+1044x^269+132x^270+300x^271+468x^272+348x^273+12x^274+108x^275+108x^276+36x^277+24x^280+30x^284+21x^288+6x^292+6x^296+3x^300

The gray image is a linear code over GF(4) with n=340, k=8 and d=236.
This code was found by Heurico 1.16 in 27.6 seconds.