The generator matrix

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

generates a code of length 90 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+294x^248+600x^249+408x^250+1080x^251+1719x^252+2676x^253+1656x^254+3384x^255+3702x^256+5772x^257+2868x^258+6036x^259+6609x^260+8148x^261+5220x^262+8232x^263+9603x^264+10668x^265+6624x^266+10404x^267+12498x^268+13836x^269+7788x^270+12768x^271+13776x^272+14760x^273+8040x^274+11688x^275+11541x^276+12120x^277+6204x^278+8508x^279+7899x^280+7308x^281+3144x^282+3948x^283+2988x^284+3048x^285+828x^286+1248x^287+837x^288+804x^289+228x^290+252x^291+129x^292+108x^293+36x^295+27x^296+24x^297+24x^300+12x^304+9x^308+9x^312+3x^316

The gray image is a linear code over GF(4) with n=360, k=9 and d=248.
This code was found by Heurico 1.16 in 435 seconds.