The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+252x^253+636x^254+624x^255+669x^256+1668x^257+1752x^258+1692x^259+1227x^260+2736x^261+2244x^262+2436x^263+1629x^264+3576x^265+3264x^266+2412x^267+1803x^268+3516x^269+3096x^270+2616x^271+1575x^272+3612x^273+2628x^274+2340x^275+1425x^276+2940x^277+2412x^278+1704x^279+999x^280+2172x^281+1668x^282+936x^283+717x^284+756x^285+576x^286+540x^287+183x^288+252x^289+144x^290+60x^291+12x^292+24x^293+12x^294

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 28.8 seconds.