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

generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 262.

Homogenous weight enumerator: w(x)=1x^0+216x^262+132x^263+369x^264+336x^265+564x^266+336x^267+276x^268+204x^269+348x^270+144x^271+120x^272+108x^273+192x^274+48x^275+120x^276+24x^277+60x^278+48x^279+63x^280+36x^281+48x^282+12x^283+24x^284+48x^285+12x^286+12x^287+12x^288+84x^290+36x^291+36x^292+12x^293+12x^294+3x^304

The gray image is a linear code over GF(4) with n=360, k=6 and d=262.
This code was found by Heurico 1.16 in 0.203 seconds.