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

generates a code of length 88 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 247.

Homogenous weight enumerator: w(x)=1x^0+468x^247+480x^248+360x^249+660x^250+2112x^251+1629x^252+816x^253+1476x^254+3624x^255+2484x^256+1044x^257+1632x^258+5088x^259+2730x^260+1392x^261+1656x^262+4788x^263+3150x^264+1116x^265+1788x^266+4704x^267+3207x^268+1332x^269+1536x^270+3972x^271+2175x^272+948x^273+1176x^274+2904x^275+1356x^276+480x^277+600x^278+1200x^279+600x^280+180x^281+216x^282+264x^283+102x^284+12x^285+12x^286+60x^287+6x^288

The gray image is a linear code over GF(4) with n=352, k=8 and d=247.
This code was found by Heurico 1.16 in 27.9 seconds.