The generator matrix

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

generates a code of length 89 over F4[X]/(X^2) who´s minimum homogenous weight is 255.

Homogenous weight enumerator: w(x)=1x^0+948x^255+375x^256+2424x^259+852x^260+2232x^263+975x^264+2184x^267+591x^268+1632x^271+375x^272+1260x^275+486x^276+900x^279+288x^280+492x^283+135x^284+192x^287+15x^288+24x^291+3x^296

The gray image is a linear code over GF(4) with n=356, k=7 and d=255.
This code was found by Heurico 1.16 in 1.45 seconds.