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

generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 269.

Homogenous weight enumerator: w(x)=1x^0+72x^269+144x^270+24x^273+3x^280+6x^284+6x^296

The gray image is a linear code over GF(4) with n=360, k=4 and d=269.
This code was found by Heurico 1.16 in 0.11 seconds.