The generator matrix

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

generates a code of length 84 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 235.

Homogenous weight enumerator: w(x)=1x^0+300x^235+492x^236+216x^237+912x^238+1620x^239+1962x^240+468x^241+1428x^242+3228x^243+3027x^244+1128x^245+2268x^246+4140x^247+3357x^248+1176x^249+2328x^250+4140x^251+3378x^252+972x^253+2532x^254+4224x^255+3639x^256+828x^257+1980x^258+3636x^259+2718x^260+840x^261+1440x^262+2076x^263+1605x^264+408x^265+732x^266+984x^267+630x^268+108x^269+192x^270+228x^271+180x^272+12x^274+3x^276

The gray image is a linear code over GF(4) with n=336, k=8 and d=235.
This code was found by Heurico 1.16 in 24.8 seconds.