The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1 (a+1)X  1  1  1  1 (a+1)X  1  1  0  1  1  1  1  0  1  1 (a+1)X  0  1  1 aX  1  1 (a+1)X  X  1  1  1  1  1  1  1 aX aX  1  1 (a+1)X  1  1  1 (a+1)X  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1 aX  1  1  1 (a+1)X  1  X  1  1  0  1  1  1  1  1  1  1  X  1  1  1  0
 0  1  0  0  0 (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  a  a  1 (a+1)X+a (a+1)X+a+1  1 a+1  1 (a+1)X+a+1 (a+1)X+1  1 aX+1 aX+1 aX+a+1 aX+a aX aX+1 X+a+1  1  1 aX+1 (a+1)X+a  1 aX+a (a+1)X  1  1 aX aX X+a+1 (a+1)X+a+1 (a+1)X (a+1)X+a (a+1)X+a  1  1 X+a aX+1  1 (a+1)X+a a+1 (a+1)X+1  0 X+1 a+1 a+1  1 (a+1)X+1 aX X+a (a+1)X aX aX a+1 aX (a+1)X+1 X+1 (a+1)X+1  1 X+a (a+1)X+a  a  1  X  1 aX+1  X  1 X+a  X (a+1)X+1  0 X+1 (a+1)X+a (a+1)X+a+1 (a+1)X aX+a+1 (a+1)X X+a  1
 0  0  1  1  a a+1 X+a+1 a+1 X+a+1  a X+a  0 a+1 X+1  0  1  1  1 X+a  X  a aX+a  X X+a X+1  1 X+a+1 X+a+1 (a+1)X aX+1 (a+1)X+1 (a+1)X+a+1 (a+1)X  X (a+1)X+a (a+1)X+a X+a+1 a+1 (a+1)X+1  0 (a+1)X+1 (a+1)X X+1 aX+a X+1 X+a  a X+1 X+a+1 aX+a+1  1  0  1 aX+a X+a (a+1)X+1  a aX aX (a+1)X  X (a+1)X+1 aX+a (a+1)X  0 (a+1)X+a+1 aX  a X+a  0  a X+a+1 (a+1)X+1 X+a X+1 aX+1 X+a+1 (a+1)X  1 (a+1)X+1 aX+1 (a+1)X+a+1 aX+a+1 (a+1)X+1 X+a  1 aX X+a  a  0
 0  0  0 (a+1)X  0  0  0  X (a+1)X  X aX (a+1)X  0  0  X aX aX (a+1)X  X aX aX  0 (a+1)X (a+1)X (a+1)X aX aX  0 (a+1)X aX aX  X  0 (a+1)X  X  X  X  X aX aX  0  0  0 aX  0 (a+1)X (a+1)X (a+1)X aX aX  0  X  X  X  0 (a+1)X  X (a+1)X  X  X aX  0  0 aX  X (a+1)X (a+1)X aX  0  0  X (a+1)X (a+1)X (a+1)X  0 (a+1)X  X  0 (a+1)X  0 (a+1)X  X  0 aX aX aX  X (a+1)X  X (a+1)X
 0  0  0  0  X aX aX aX aX  0 (a+1)X  X  0 (a+1)X  X  X  0  X aX (a+1)X  0  0  0 (a+1)X  0 aX  X  X aX (a+1)X (a+1)X (a+1)X aX (a+1)X (a+1)X  0 (a+1)X  0  X aX  X  X  0  X (a+1)X (a+1)X (a+1)X  X  X  0 (a+1)X (a+1)X  0 aX aX (a+1)X  X aX (a+1)X  X aX aX (a+1)X (a+1)X  X (a+1)X  X aX aX aX aX (a+1)X (a+1)X aX  X (a+1)X  X  X  X  X  0 aX  X aX  X  X  0  X  0  X

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

Homogenous weight enumerator: w(x)=1x^0+582x^252+228x^253+612x^255+2538x^256+996x^257+1116x^259+4482x^260+1404x^261+1632x^263+5916x^264+1896x^265+2136x^267+6831x^268+2352x^269+2268x^271+7092x^272+1788x^273+2148x^275+6303x^276+1788x^277+1416x^279+4341x^280+1152x^281+720x^283+2079x^284+564x^285+216x^287+627x^288+120x^289+24x^291+99x^292+27x^296+15x^300+9x^304+6x^308+3x^312+3x^316+3x^320+3x^328

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 29.5 seconds.