The generator matrix

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

generates a code of length 90 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 254.

Homogenous weight enumerator: w(x)=1x^0+132x^254+306x^256+1116x^258+531x^260+1596x^262+696x^264+2208x^266+609x^268+2196x^270+660x^272+2040x^274+582x^276+2004x^278+411x^280+768x^282+153x^284+216x^286+39x^288+12x^290+24x^292+21x^296+12x^300+21x^304+3x^308+12x^312+6x^316+9x^320

The gray image is a linear code over GF(4) with n=360, k=7 and d=254.
This code was found by Heurico 1.16 in 22.4 seconds.