The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1 a^2*X  1  1  1  0  1  1  1  1 a^2*X a*X  1  1  X  1  1  1  1 a*X  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  1 a^2*X  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  1 a^2*X  1 a^2*X  1  1  1  X  1  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2 a^2*X+1 a^2*X+1  a a^2*X+a^2 a^2*X+a  1 a^2  1  1 a^2*X+a^2  a  1  X a^2*X+a X+1 X+1  1  1  X X+a^2  1  1 X+a^2 a^2*X+a^2  X  1 a^2*X X+a X+a X+1 a^2*X+1 X+a^2 X+a^2 a*X  0 a*X  a a^2*X+a a^2*X a^2*X+a^2  1  1  1  0 a*X+a a*X+a^2 a*X+a  1 X+a^2 a^2*X+1  1  a a^2*X+1 a^2*X+a^2 X+1 a^2*X+a^2  1 a*X a*X a^2*X  0  1 X+a a*X+a^2 a^2*X+1  1 a^2*X+a^2 X+1
 0  0  1  1  a a^2  1 X+1  1  a  0  X a*X+a a^2 a^2 a*X+a^2 X+1 a^2  0 X+a  a a^2*X+1  1 X+a a^2*X+1  a X+1 a*X+a X+1 X+a^2 a^2 a*X+a^2  a a^2*X+a  X a^2*X a^2*X+a a^2*X+a^2 a^2*X X+1  0  a a^2*X+a^2 X+1  X a*X X+a  1 X+a X+a a^2*X+a^2 a^2*X+1 a^2 a*X a^2*X+a^2 X+a a^2*X+a^2 a^2*X+1  a a^2*X+a X+1 a^2*X a*X a*X+a^2  1 X+a^2  1 a^2*X+a^2  1 a*X+a^2 X+a a^2*X+a  1 X+a a*X  1 a*X+a^2
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a*X a^2*X a^2*X a*X a*X  X a^2*X a*X  X a*X  0 a^2*X a*X a*X a*X a*X  0  0  0 a^2*X  0  X  X a*X a^2*X a*X a*X  0  X a^2*X  0 a*X a^2*X a^2*X  0 a^2*X a^2*X a*X a^2*X a^2*X a^2*X  0  0 a^2*X  0 a*X  0  X  0 a*X  0  0 a*X a*X  0 a^2*X  X  X a^2*X  X a^2*X a*X  X  0 a*X
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  0  X a*X a*X  X a^2*X  X a*X  0 a*X  0  0  0  0 a*X a^2*X  X  X  0 a*X a^2*X  X  X  0  0 a^2*X a^2*X a^2*X a*X  X a*X  X a^2*X  0 a^2*X  X a^2*X a^2*X a^2*X a^2*X a*X a*X  0 a*X a*X  X  0 a^2*X a^2*X a*X  X a^2*X a^2*X  X  0  X  0  X  0  0 a*X a^2*X a*X a*X a*X

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

Homogenous weight enumerator: w(x)=1x^0+96x^213+408x^214+324x^215+729x^216+600x^217+1812x^218+924x^219+1629x^220+1236x^221+2544x^222+1452x^223+2151x^224+1752x^225+3696x^226+2208x^227+2607x^228+2268x^229+4656x^230+2244x^231+3207x^232+2460x^233+4728x^234+2232x^235+3024x^236+2088x^237+3744x^238+1956x^239+2088x^240+1296x^241+2208x^242+768x^243+651x^244+444x^245+744x^246+168x^247+195x^248+36x^249+36x^250+12x^251+21x^252+12x^253+27x^256+18x^260+6x^264+15x^268+9x^272+3x^280+3x^284

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 24.4 seconds.