The generator matrix

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

generates a code of length 87 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+864x^240+612x^241+1008x^242+1020x^243+2862x^244+2088x^245+2832x^246+2100x^247+6552x^248+4296x^249+5136x^250+3384x^251+10389x^252+7020x^253+7716x^254+5028x^255+15201x^256+10056x^257+9744x^258+5988x^259+17955x^260+11556x^261+12120x^262+7092x^263+19506x^264+11232x^265+10596x^266+5892x^267+15336x^268+8544x^269+7392x^270+4188x^271+9189x^272+4356x^273+3576x^274+1728x^275+3663x^276+1404x^277+1128x^278+408x^279+753x^280+264x^281+180x^282+36x^283+69x^284+12x^285+12x^286+21x^288+21x^292+9x^296+6x^300+3x^308

The gray image is a linear code over GF(4) with n=348, k=9 and d=240.
This code was found by Heurico 1.16 in 589 seconds.