The generator matrix

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

generates a code of length 71 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 201.

Homogenous weight enumerator: w(x)=1x^0+420x^201+660x^202+216x^203+42x^204+1260x^205+1380x^206+492x^207+45x^208+1332x^209+1368x^210+528x^211+57x^212+1212x^213+1152x^214+456x^215+57x^216+1140x^217+1044x^218+300x^219+24x^220+864x^221+708x^222+240x^223+6x^224+504x^225+480x^226+60x^227+12x^228+168x^229+120x^230+12x^231+3x^232+12x^233+6x^236+3x^244

The gray image is a linear code over GF(4) with n=284, k=7 and d=201.
This code was found by Heurico 1.16 in 1.31 seconds.