The generator matrix

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

generates a code of length 90 over F4[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+345x^252+384x^253+384x^254+204x^255+1932x^256+1488x^257+1080x^258+648x^259+3117x^260+2028x^261+1644x^262+792x^263+4149x^264+3168x^265+1812x^266+1056x^267+4626x^268+2916x^269+2244x^270+1320x^271+4866x^272+3072x^273+2076x^274+1008x^275+4659x^276+2580x^277+1848x^278+648x^279+3150x^280+1824x^281+828x^282+336x^283+1227x^284+732x^285+276x^286+108x^287+399x^288+240x^289+60x^290+24x^291+117x^292+36x^294+33x^296+18x^300+12x^304+3x^308+12x^312+6x^320

The gray image is a linear code over GF(4) with n=360, k=8 and d=252.
This code was found by Heurico 1.16 in 28 seconds.