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

generates a code of length 85 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+288x^240+324x^241+144x^242+780x^244+684x^245+372x^246+1035x^248+828x^249+564x^250+1272x^252+1260x^253+600x^254+1179x^256+1056x^257+600x^258+1167x^260+1140x^261+516x^262+969x^264+540x^265+228x^266+270x^268+276x^269+48x^270+87x^272+36x^273+27x^276+36x^280+15x^284+15x^288+18x^292+3x^300+6x^304

The gray image is a linear code over GF(4) with n=340, k=7 and d=240.
This code was found by Heurico 1.16 in 56.9 seconds.