The generator matrix

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

generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 245.

Homogenous weight enumerator: w(x)=1x^0+768x^245+1320x^246+528x^247+108x^248+2316x^249+2664x^250+1176x^251+114x^252+4140x^253+4212x^254+1440x^255+96x^256+4380x^257+4548x^258+1512x^259+183x^260+4704x^261+4764x^262+1608x^263+270x^264+4608x^265+4344x^266+1188x^267+141x^268+3372x^269+3264x^270+1188x^271+63x^272+2352x^273+1740x^274+468x^275+33x^276+828x^277+732x^278+84x^279+3x^280+120x^281+48x^282+24x^283+9x^284+60x^285+12x^286+3x^296

The gray image is a linear code over GF(4) with n=348, k=8 and d=245.
This code was found by Heurico 1.16 in 887 seconds.