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  1  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  a a^2*X+1  a  0 a^2 a*X+1
 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  1  0  X  a a^2*X+1  1
 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  0  X a^2*X a^2*X  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+828x^255+522x^256+2316x^259+921x^260+2364x^263+720x^264+2400x^267+552x^268+1680x^271+492x^272+1128x^275+339x^276+876x^279+291x^280+576x^283+186x^284+108x^287+51x^288+12x^291+18x^292+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 1.79 seconds.