The generator matrix

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

generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 213.

Homogenous weight enumerator: w(x)=1x^0+252x^213+288x^214+180x^215+396x^216+1104x^217+1380x^218+768x^219+693x^220+2964x^221+2580x^222+1248x^223+1032x^224+4164x^225+3084x^226+1440x^227+1185x^228+5100x^229+4236x^230+1812x^231+1317x^232+5232x^233+4248x^234+1680x^235+1164x^236+4812x^237+3180x^238+1224x^239+711x^240+2868x^241+1836x^242+624x^243+426x^244+984x^245+564x^246+240x^247+120x^248+168x^249+108x^250+51x^252+18x^256+9x^260+12x^264+24x^268+6x^272+3x^280

The gray image is a linear code over GF(4) with n=308, k=8 and d=213.
This code was found by Heurico 1.16 in 25.7 seconds.