The generator matrix

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

generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+624x^265+564x^266+396x^267+459x^268+2232x^269+2184x^270+1140x^271+1038x^272+3444x^273+3000x^274+1308x^275+1053x^276+4260x^277+3384x^278+1476x^279+990x^280+4440x^281+3540x^282+1428x^283+1251x^284+4392x^285+3312x^286+1464x^287+1041x^288+4020x^289+2904x^290+1080x^291+759x^292+2700x^293+1656x^294+636x^295+366x^296+1032x^297+720x^298+192x^299+174x^300+432x^301+216x^302+84x^303+36x^304+72x^305+24x^306+12x^307

The gray image is a linear code over GF(4) with n=376, k=8 and d=265.
This code was found by Heurico 1.16 in 33 seconds.