The generator matrix

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

generates a code of length 71 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 206.

Homogenous weight enumerator: w(x)=1x^0+588x^206+480x^207+75x^208+672x^210+528x^211+84x^212+420x^214+180x^215+66x^216+240x^218+132x^219+12x^220+180x^222+108x^223+144x^226+60x^227+60x^230+48x^231+15x^232+3x^248

The gray image is a linear code over GF(4) with n=284, k=6 and d=206.
This code was found by Heurico 1.16 in 3.59 seconds.