The generator matrix

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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 259.

Homogenous weight enumerator: w(x)=1x^0+192x^259+399x^260+312x^261+72x^262+540x^263+579x^264+324x^265+84x^266+264x^267+183x^268+120x^269+72x^271+96x^272+60x^273+24x^274+108x^275+138x^276+72x^277+96x^279+144x^280+24x^281+12x^283+60x^284+48x^285+60x^287+12x^290

The gray image is a linear code over GF(4) with n=356, k=6 and d=259.
This code was found by Heurico 1.16 in 0.168 seconds.