The generator matrix

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

generates a code of length 78 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+186x^216+336x^217+120x^218+612x^219+1428x^220+1596x^221+264x^222+1356x^223+2520x^224+2364x^225+348x^226+2040x^227+3750x^228+3312x^229+480x^230+2712x^231+4761x^232+3972x^233+516x^234+2940x^235+4896x^236+3744x^237+552x^238+2952x^239+4119x^240+3636x^241+516x^242+1872x^243+2760x^244+1776x^245+240x^246+744x^247+906x^248+636x^249+36x^250+120x^251+168x^252+132x^253+12x^255+33x^256+33x^260+15x^264+9x^268+3x^272+9x^276+3x^284

The gray image is a linear code over GF(4) with n=312, k=8 and d=216.
This code was found by Heurico 1.16 in 23.1 seconds.