The generator matrix

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

generates a code of length 90 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 262.

Homogenous weight enumerator: w(x)=1x^0+288x^262+240x^263+234x^264+132x^265+684x^266+468x^267+138x^268+156x^269+396x^270+192x^271+126x^272+48x^273+252x^274+72x^275+51x^276+24x^277+108x^278+60x^279+9x^280+72x^282+48x^283+60x^284+60x^286+36x^287+3x^288+12x^289+24x^290+36x^291+15x^292+12x^293+36x^294+3x^296

The gray image is a linear code over GF(4) with n=360, k=6 and d=262.
This code was found by Heurico 1.16 in 0.219 seconds.