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

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+564x^227+522x^228+744x^229+1056x^230+2232x^231+1332x^232+1320x^233+2112x^234+3456x^235+1713x^236+2016x^237+2700x^238+3876x^239+2358x^240+2364x^241+2604x^242+4476x^243+2541x^244+1824x^245+2664x^246+3912x^247+2274x^248+1848x^249+2064x^250+3204x^251+1635x^252+1356x^253+1620x^254+2112x^255+705x^256+648x^257+420x^258+636x^259+213x^260+156x^261+120x^262+108x^263+18x^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 57.2 seconds.