The generator matrix

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

generates a code of length 92 over F4[X]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+1362x^264+2970x^268+3273x^272+2712x^276+2280x^280+1632x^284+1137x^288+696x^292+306x^296+6x^300+9x^304

The gray image is a linear code over GF(4) with n=368, k=7 and d=264.
This code was found by Heurico 1.16 in 1.8 seconds.