The generator matrix

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

generates a code of length 86 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 236.

Homogenous weight enumerator: w(x)=1x^0+330x^236+372x^237+432x^238+828x^239+2283x^240+2112x^241+1212x^242+2508x^243+5268x^244+4416x^245+2784x^246+4632x^247+9390x^248+6816x^249+4248x^250+6492x^251+14391x^252+9816x^253+5520x^254+9672x^255+17112x^256+11880x^257+7152x^258+10452x^259+19983x^260+12672x^261+6840x^262+9864x^263+17301x^264+10884x^265+4776x^266+6564x^267+10494x^268+5652x^269+2832x^270+3324x^271+4674x^272+2352x^273+852x^274+864x^275+954x^276+576x^277+216x^278+96x^279+150x^280+36x^281+27x^284+15x^288+3x^292+15x^296+6x^300+3x^304

The gray image is a linear code over GF(4) with n=344, k=9 and d=236.
This code was found by Heurico 1.16 in 474 seconds.