The generator matrix

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

generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 215.

Homogenous weight enumerator: w(x)=1x^0+492x^215+720x^216+744x^217+696x^218+1704x^219+1905x^220+1800x^221+1188x^222+3156x^223+2847x^224+2400x^225+1416x^226+3444x^227+3282x^228+2748x^229+1632x^230+3648x^231+3558x^232+2688x^233+1812x^234+3924x^235+3348x^236+2556x^237+1368x^238+3000x^239+2292x^240+1692x^241+804x^242+1680x^243+1194x^244+624x^245+276x^246+408x^247+294x^248+108x^249+24x^250+48x^251+15x^252

The gray image is a linear code over GF(4) with n=308, k=8 and d=215.
This code was found by Heurico 1.16 in 24.2 seconds.