The generator matrix

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

generates a code of length 78 over F4[X]/(X^2) who´s minimum homogenous weight is 227.

Homogenous weight enumerator: w(x)=1x^0+756x^227+270x^228+960x^231+348x^232+588x^235+192x^236+348x^239+84x^240+156x^243+75x^244+96x^247+36x^248+84x^251+12x^252+84x^255+3x^260+3x^272

The gray image is a linear code over GF(4) with n=312, k=6 and d=227.
This code was found by Heurico 1.16 in 0.203 seconds.