The generator matrix

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

generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 242.

Homogenous weight enumerator: w(x)=1x^0+108x^242+96x^243+36x^246+6x^248+3x^260+3x^264+3x^276

The gray image is a linear code over GF(4) with n=324, k=4 and d=242.
This code was found by Heurico 1.16 in 0.078 seconds.