The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  1 a^2*X a*X  1  1  1  1 a*X  1  1  1  1  1  1  1  1 a^2*X  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1  X  X  1  1  1  1 a*X a*X  1  1  1  1  0  X  1  1  1 a^2*X  X a^2*X  1
 0  1  0  0  0  X  X a^2*X+1 a*X+1  1 a^2*X+a a*X+a a*X+a^2 X+a^2 a^2*X+a^2  a a*X a^2*X+a a*X+a^2  1 a*X a^2*X+a a^2*X+1 a*X  1 a*X+1 a^2 X+a a*X+a  1 a*X+a  1 a*X+1 X+a X+a^2  1  1 X+a X+a a^2*X+a^2  0  X X+1 a*X+a^2  0  1  a a*X+a^2  0 X+a^2  1  1  1  1 a^2*X+1 a^2*X+a^2  1 X+1 a*X+a a^2  0 a^2*X  a a^2 X+a a*X  1  1 a^2*X a*X  1 a^2*X a^2*X+a a^2*X+a^2 a^2*X+a  1  1 a^2*X+a a^2*X+1 a*X+a X+1 a*X  1 a^2 a^2*X+1 a*X  1  0  1  X
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a a^2*X  a a*X+1  a a*X+a a^2 a*X+a X+a  a a^2*X+1  1 a^2*X+1 a^2*X+a^2 X+1 a^2*X a*X X+a a^2  1 X+a a^2*X+a^2 X+1 a^2*X X+a^2  0  0  1 a^2*X+1 a^2*X a^2*X a*X+a^2 a^2  0  1 a^2*X+a a^2 a^2*X+a  a a^2*X+a^2  0  a a^2*X a^2*X a^2*X+a a^2*X+a^2 a^2*X+a X+1 a*X+a^2  a a*X X+1  X a^2*X X+a^2 X+a  0 X+a^2 X+a a^2*X a^2*X  1  1 X+a a*X+a^2 a^2*X+a^2 a*X+a a*X+a^2 a^2*X+a^2 a^2*X  a  0 a*X a*X+1  1 a^2*X a^2*X+a^2 a*X+a a*X+a^2  1  1  1  0
 0  0  0  1 a^2  a  1 a*X X+a  a  X a*X+a^2 a^2*X+1 a*X  0  X a^2 X+a^2  a  1 X+a a^2*X+a a^2*X X+1  a  X a^2*X+1 a*X+1 X+a a*X+a  X a^2*X+1 a*X+1 X+a a^2*X X+a a^2*X+a^2 X+a^2 a^2*X X+1 a^2*X+a^2 X+1 a*X+1  a  X a*X+a^2 a*X+1 a^2*X+a^2 X+1  a a^2*X+1  X a*X+a a*X+1 X+a^2 a*X+1  X  1 a^2*X+a a*X+1 X+a^2  a a*X+a a*X a^2*X+1 a^2*X+1  a a^2*X+a  a  X a^2*X+1 X+1 a*X+a^2 a^2*X+a^2 X+a^2  X a^2*X+a^2 X+1 a^2 a^2*X+a^2 a*X+a  X a^2 a*X+a^2 a^2*X+a X+a^2 a^2 a*X+a a*X+a  X
 0  0  0  0  X  0 a*X  0  0  0  X  X a*X a*X  X a^2*X a^2*X a^2*X  0  0  X a*X a*X  X a*X a^2*X  X  X a^2*X a^2*X  X a*X a^2*X a*X  0  0  X a*X  X  0 a*X a^2*X a^2*X a^2*X a*X  0 a^2*X  X a^2*X  0 a^2*X a^2*X  0  X a^2*X  X a*X a*X a^2*X  X  X a*X a*X  X  X a*X  X a*X a^2*X a^2*X a*X  X  X a*X a*X  0 a*X  0  X a^2*X  0  X a^2*X a*X a*X a*X a*X a*X  0 a^2*X

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

Homogenous weight enumerator: w(x)=1x^0+255x^248+600x^249+360x^250+1476x^251+1701x^252+2292x^253+1656x^254+3744x^255+4077x^256+4332x^257+3480x^258+6444x^259+6834x^260+6804x^261+4584x^262+9996x^263+9042x^264+9564x^265+6864x^266+13260x^267+12477x^268+11952x^269+7764x^270+15072x^271+13551x^272+12180x^273+8088x^274+13356x^275+12009x^276+10404x^277+5520x^278+9972x^279+7221x^280+6252x^281+3192x^282+4752x^283+3369x^284+2580x^285+1308x^286+1608x^287+849x^288+576x^289+192x^290+168x^291+201x^292+48x^293+24x^295+36x^296+27x^300+18x^304+6x^308+6x^320

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 413 seconds.