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

generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 253.

Homogenous weight enumerator: w(x)=1x^0+240x^253+336x^254+408x^255+174x^256+228x^257+444x^258+456x^259+114x^260+204x^261+228x^262+240x^263+81x^264+60x^265+108x^266+72x^267+48x^268+108x^269+108x^270+48x^271+60x^273+48x^274+72x^275+3x^276+48x^277+48x^278+24x^279+12x^280+12x^281+24x^282+24x^283+12x^284+3x^300

The gray image is a linear code over GF(4) with n=348, k=6 and d=253.
This code was found by Heurico 1.16 in 428 seconds.