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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 255.

Homogenous weight enumerator: w(x)=1x^0+972x^255+381x^256+2352x^259+846x^260+2352x^263+723x^264+2028x^267+951x^268+1704x^271+441x^272+1440x^275+372x^276+696x^279+180x^280+468x^283+135x^284+228x^287+63x^288+48x^291+3x^296

The gray image is a linear code over GF(4) with n=356, k=7 and d=255.
This code was found by Heurico 1.16 in 1.73 seconds.