The generator matrix

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

generates a code of length 71 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 205.

Homogenous weight enumerator: w(x)=1x^0+144x^205+264x^207+1251x^208+180x^209+264x^211+642x^212+156x^213+48x^215+54x^216+180x^217+6x^220+36x^221+168x^223+558x^224+72x^225+24x^227+42x^228+6x^236

The gray image is a linear code over GF(4) with n=284, k=6 and d=205.
This code was found by Heurico 1.16 in 18.7 seconds.