The generator matrix

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

generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+264x^244+612x^245+384x^246+756x^247+1458x^248+2100x^249+912x^250+2112x^251+2547x^252+3012x^253+1440x^254+2280x^255+3156x^256+3216x^257+1452x^258+2604x^259+3198x^260+3636x^261+1692x^262+2520x^263+3159x^264+3384x^265+1452x^266+2592x^267+2886x^268+3036x^269+1104x^270+1512x^271+1785x^272+1632x^273+492x^274+732x^275+726x^276+744x^277+276x^278+228x^279+243x^280+132x^281+12x^282+24x^283+27x^284+6x^288

The gray image is a linear code over GF(4) with n=348, k=8 and d=244.
This code was found by Heurico 1.16 in 27.6 seconds.