The generator matrix

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

generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 253.

Homogenous weight enumerator: w(x)=1x^0+324x^253+588x^254+792x^255+630x^256+1548x^257+1908x^258+1956x^259+1104x^260+2328x^261+2544x^262+2436x^263+1122x^264+3300x^265+3468x^266+2664x^267+1383x^268+3624x^269+3312x^270+2724x^271+1644x^272+3036x^273+3108x^274+2556x^275+1278x^276+2844x^277+2568x^278+2220x^279+897x^280+1956x^281+1680x^282+960x^283+495x^284+756x^285+624x^286+468x^287+135x^288+240x^289+156x^290+120x^291+12x^292+12x^293+12x^294+3x^296

The gray image is a linear code over GF(4) with n=360, k=8 and d=253.
This code was found by Heurico 1.16 in 29.1 seconds.