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

generates a code of length 95 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 278.

Homogenous weight enumerator: w(x)=1x^0+864x^278+462x^280+864x^282+276x^284+564x^286+93x^288+276x^290+60x^292+180x^294+39x^296+168x^298+36x^300+108x^302+42x^304+36x^306+12x^308+12x^310+3x^328

The gray image is a linear code over GF(4) with n=380, k=6 and d=278.
This code was found by Heurico 1.16 in 49.5 seconds.