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

generates a code of length 91 over F4[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+264x^265+168x^266+372x^267+105x^268+720x^269+300x^270+372x^271+63x^272+444x^273+108x^274+192x^275+24x^276+204x^277+60x^278+36x^279+12x^280+84x^281+84x^282+96x^283+33x^284+84x^285+12x^286+36x^287+12x^288+12x^289+36x^291+3x^292+72x^293+36x^294+12x^295+36x^297+3x^308

The gray image is a linear code over GF(4) with n=364, k=6 and d=265.
This code was found by Heurico 1.16 in 0.218 seconds.