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

generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 222.

Homogenous weight enumerator: w(x)=1x^0+468x^222+816x^223+729x^224+516x^225+2640x^226+2520x^227+2352x^228+1200x^229+6768x^230+5220x^231+4314x^232+2088x^233+11568x^234+8160x^235+6747x^236+3336x^237+16344x^238+11580x^239+8868x^240+4572x^241+20304x^242+14028x^243+10260x^244+5028x^245+22140x^246+14280x^247+9945x^248+4248x^249+17052x^250+10080x^251+6372x^252+2592x^253+9660x^254+5244x^255+2643x^256+840x^257+3144x^258+1476x^259+810x^260+132x^261+492x^262+300x^263+126x^264+24x^265+12x^266+24x^267+24x^268+24x^272+15x^276+3x^280+9x^284+3x^288+3x^292

The gray image is a linear code over GF(4) with n=324, k=9 and d=222.
This code was found by Heurico 1.16 in 357 seconds.