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

generates a code of length 65 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 188.

Homogenous weight enumerator: w(x)=1x^0+312x^188+696x^189+252x^190+108x^191+288x^192+600x^193+144x^194+48x^195+279x^196+288x^197+84x^198+141x^200+288x^201+24x^202+135x^204+108x^205+24x^206+36x^207+24x^208+96x^209+48x^210+24x^212+36x^213+6x^220+6x^224

The gray image is a linear code over GF(4) with n=260, k=6 and d=188.
This code was found by Heurico 1.16 in 0.094 seconds.