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

generates a code of length 88 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 256.

Homogenous weight enumerator: w(x)=1x^0+213x^256+372x^257+348x^258+132x^259+510x^260+264x^261+396x^262+132x^263+234x^264+204x^265+216x^266+72x^267+195x^268+84x^269+72x^270+12x^271+81x^272+144x^273+24x^274+12x^275+96x^276+24x^277+24x^278+24x^279+60x^280+24x^281+36x^282+12x^284+36x^285+36x^286+3x^288+3x^316

The gray image is a linear code over GF(4) with n=352, k=6 and d=256.
This code was found by Heurico 1.16 in 0.162 seconds.