The generator matrix

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

generates a code of length 76 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 216.

Homogenous weight enumerator: w(x)=1x^0+465x^216+648x^217+384x^218+1224x^220+1164x^221+684x^222+1449x^224+1176x^225+708x^226+1395x^228+996x^229+396x^230+1107x^232+1092x^233+372x^234+702x^236+588x^237+288x^238+528x^240+312x^241+216x^242+246x^244+132x^245+24x^246+42x^248+36x^249+6x^252+3x^260

The gray image is a linear code over GF(4) with n=304, k=7 and d=216.
This code was found by Heurico 1.16 in 1.41 seconds.