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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 259.

Homogenous weight enumerator: w(x)=1x^0+252x^259+207x^260+180x^261+276x^262+660x^263+519x^264+168x^265+108x^266+408x^267+237x^268+96x^269+84x^270+84x^271+54x^272+72x^273+36x^274+108x^275+93x^276+24x^277+36x^278+120x^279+30x^280+24x^281+24x^282+12x^283+24x^284+12x^285+12x^286+48x^287+48x^288+36x^291+3x^308

The gray image is a linear code over GF(4) with n=356, k=6 and d=259.
This code was found by Heurico 1.16 in 0.203 seconds.