The generator matrix

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

generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 227.

Homogenous weight enumerator: w(x)=1x^0+696x^227+558x^228+732x^229+840x^230+2076x^231+1914x^232+1704x^233+1188x^234+3060x^235+2484x^236+2100x^237+1968x^238+3552x^239+3213x^240+2496x^241+1896x^242+4164x^243+3267x^244+2460x^245+1992x^246+3756x^247+2874x^248+1932x^249+1536x^250+3084x^251+2334x^252+1476x^253+924x^254+1944x^255+948x^256+768x^257+324x^258+612x^259+285x^260+144x^261+84x^262+96x^263+42x^264+12x^265

The gray image is a linear code over GF(4) with n=324, k=8 and d=227.
This code was found by Heurico 1.16 in 81.6 seconds.