The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+312x^185+480x^186+384x^187+903x^188+1572x^189+1692x^190+1212x^191+1941x^192+2448x^193+2556x^194+1728x^195+2838x^196+3624x^197+3372x^198+1932x^199+3276x^200+4080x^201+3552x^202+2184x^203+3225x^204+3432x^205+3624x^206+1884x^207+2676x^208+2880x^209+2352x^210+1032x^211+1164x^212+1224x^213+672x^214+348x^215+300x^216+360x^217+132x^218+48x^219+54x^220+36x^221+6x^224

The gray image is a linear code over GF(4) with n=268, k=8 and d=185.
This code was found by Heurico 1.16 in 20.1 seconds.