The generator matrix

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

generates a code of length 78 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 213.

Homogenous weight enumerator: w(x)=1x^0+180x^213+600x^214+612x^215+1320x^216+1728x^217+2124x^218+2256x^219+3300x^220+3888x^221+5364x^222+3948x^223+6048x^224+7344x^225+8196x^226+7272x^227+9213x^228+9648x^229+12036x^230+9528x^231+11706x^232+12828x^233+14760x^234+11184x^235+12711x^236+13284x^237+13464x^238+10572x^239+11289x^240+10920x^241+10824x^242+6744x^243+6669x^244+5748x^245+4860x^246+2652x^247+2685x^248+1740x^249+1212x^250+480x^251+471x^252+276x^253+252x^254+48x^255+48x^256+36x^258+24x^260+24x^264+9x^268+12x^272+3x^280+3x^284

The gray image is a linear code over GF(4) with n=312, k=9 and d=213.
This code was found by Heurico 1.16 in 325 seconds.