The generator matrix

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

generates a code of length 82 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 228.

Homogenous weight enumerator: w(x)=1x^0+255x^228+240x^229+156x^230+504x^231+1980x^232+804x^233+576x^234+1344x^235+3813x^236+1308x^237+696x^238+1500x^239+5181x^240+2040x^241+996x^242+2028x^243+5952x^244+2184x^245+1260x^246+2172x^247+6432x^248+2412x^249+984x^250+2352x^251+5676x^252+1752x^253+816x^254+1716x^255+3663x^256+1104x^257+516x^258+492x^259+1251x^260+360x^261+144x^262+156x^263+429x^264+72x^265+24x^267+99x^268+12x^269+24x^272+27x^276+15x^280+9x^284+3x^288+3x^292+3x^300

The gray image is a linear code over GF(4) with n=328, k=8 and d=228.
This code was found by Heurico 1.16 in 26.6 seconds.