The generator matrix

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

generates a code of length 88 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 242.

Homogenous weight enumerator: w(x)=1x^0+276x^242+504x^243+381x^244+1068x^245+1800x^246+2556x^247+1548x^248+3096x^249+3924x^250+5532x^251+2739x^252+5148x^253+6876x^254+8508x^255+4998x^256+7692x^257+9540x^258+13104x^259+6501x^260+9696x^261+12804x^262+15660x^263+7482x^264+11172x^265+13968x^266+15480x^267+7623x^268+10860x^269+12384x^270+12840x^271+5508x^272+7800x^273+7824x^274+8280x^275+2988x^276+3516x^277+3468x^278+2880x^279+933x^280+1116x^281+756x^282+588x^283+171x^284+240x^285+108x^286+84x^287+21x^288+36x^289+24x^292+18x^296+12x^300+6x^308+3x^312+3x^316

The gray image is a linear code over GF(4) with n=352, k=9 and d=242.
This code was found by Heurico 1.16 in 414 seconds.