The generator matrix

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

generates a code of length 93 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 257.

Homogenous weight enumerator: w(x)=1x^0+528x^257+768x^258+492x^259+1113x^260+1836x^261+3000x^262+1824x^263+2562x^264+4188x^265+6012x^266+3072x^267+4824x^268+7440x^269+8400x^270+4572x^271+6189x^272+11256x^273+12024x^274+6444x^275+8634x^276+13296x^277+14748x^278+8472x^279+9816x^280+14820x^281+15888x^282+7716x^283+8988x^284+12876x^285+12540x^286+5808x^287+6297x^288+8136x^289+8376x^290+3432x^291+3339x^292+3996x^293+3276x^294+984x^295+1221x^296+1368x^297+900x^298+156x^299+177x^300+108x^301+84x^302+36x^303+18x^304+24x^305+36x^308+12x^312+3x^316+9x^320+3x^328+6x^332

The gray image is a linear code over GF(4) with n=372, k=9 and d=257.
This code was found by Heurico 1.16 in 429 seconds.