The generator matrix

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

generates a code of length 92 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 259.

Homogenous weight enumerator: w(x)=1x^0+444x^259+483x^260+732x^261+708x^262+1968x^263+1824x^264+1356x^265+1428x^266+2988x^267+2280x^268+2004x^269+1380x^270+3360x^271+2949x^272+2232x^273+1944x^274+3588x^275+3171x^276+2400x^277+1920x^278+3912x^279+2688x^280+2148x^281+1524x^282+3264x^283+2196x^284+1632x^285+972x^286+2100x^287+1644x^288+972x^289+588x^290+1068x^291+480x^292+288x^293+240x^294+324x^295+174x^296+60x^297+36x^298+24x^299+30x^300+12x^302

The gray image is a linear code over GF(4) with n=368, k=8 and d=259.
This code was found by Heurico 1.16 in 27.9 seconds.