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

generates a code of length 87 over F4[X]/(X^2) who´s minimum homogenous weight is 254.

Homogenous weight enumerator: w(x)=1x^0+588x^254+504x^255+99x^256+672x^258+564x^259+54x^260+504x^262+144x^263+66x^264+168x^266+96x^267+144x^270+108x^271+12x^272+144x^274+48x^275+6x^276+36x^278+12x^279+6x^280+48x^282+60x^283+12x^284

The gray image is a linear code over GF(4) with n=348, k=6 and d=254.
This code was found by Heurico 1.16 in 0.219 seconds.