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

generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 254.

Homogenous weight enumerator: w(x)=1x^0+672x^254+456x^255+87x^256+612x^258+540x^259+60x^260+408x^262+300x^263+78x^264+192x^266+24x^267+12x^268+240x^270+60x^271+72x^274+96x^275+48x^278+48x^279+15x^280+60x^282+12x^283+3x^312

The gray image is a linear code over GF(4) with n=348, k=6 and d=254.
This code was found by Heurico 1.16 in 91.5 seconds.