The generator matrix

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

generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+900x^216+3012x^220+3456x^224+2964x^228+2448x^232+1740x^236+1284x^240+444x^244+132x^248+3x^256

The gray image is a linear code over GF(4) with n=304, k=7 and d=216.
This code was found by Heurico 1.16 in 1.25 seconds.