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

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

Homogenous weight enumerator: w(x)=1x^0+180x^242+564x^243+441x^244+1392x^245+1668x^246+2040x^247+1746x^248+3864x^249+3360x^250+4416x^251+3819x^252+6684x^253+6192x^254+6696x^255+5169x^256+9696x^257+8772x^258+9564x^259+7395x^260+13272x^261+12408x^262+11904x^263+8634x^264+14508x^265+13320x^266+12696x^267+8799x^268+14280x^269+10572x^270+10848x^271+5916x^272+9864x^273+7344x^274+6360x^275+3687x^276+4440x^277+2844x^278+1944x^279+999x^280+1524x^281+816x^282+480x^283+387x^284+348x^285+108x^286+72x^287+42x^288+39x^292+9x^296+3x^300+9x^304+6x^308+3x^320

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 398 seconds.