The generator matrix

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

generates a code of length 88 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 246.

Homogenous weight enumerator: w(x)=1x^0+384x^246+276x^247+426x^248+384x^249+1704x^250+1368x^251+924x^252+588x^253+3528x^254+2100x^255+1221x^256+732x^257+4524x^258+2736x^259+1698x^260+1008x^261+5376x^262+3324x^263+1662x^264+996x^265+5208x^266+3636x^267+1926x^268+1212x^269+4440x^270+2712x^271+1308x^272+756x^273+3372x^274+1560x^275+600x^276+360x^277+1632x^278+600x^279+294x^280+108x^281+456x^282+108x^283+87x^284+96x^286+12x^287+21x^288+27x^292+15x^296+15x^300+9x^304+3x^308+3x^312

The gray image is a linear code over GF(4) with n=352, k=8 and d=246.
This code was found by Heurico 1.16 in 51.1 seconds.