The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+900x^190+756x^191+186x^192+1596x^194+1188x^195+222x^196+1848x^198+1368x^199+183x^200+1788x^202+1128x^203+219x^204+1524x^206+852x^207+75x^208+900x^210+516x^211+48x^212+528x^214+288x^215+69x^216+132x^218+48x^219+15x^220+6x^224

The gray image is a linear code over GF(4) with n=268, k=7 and d=190.
This code was found by Heurico 1.16 in 9.66 seconds.