The generator matrix

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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 189.

Homogenous weight enumerator: w(x)=1x^0+636x^189+1896x^190+312x^192+2064x^193+3660x^194+504x^196+3912x^197+5568x^198+762x^200+4128x^201+7032x^202+960x^204+4968x^205+7128x^206+732x^208+4608x^209+6492x^210+504x^212+3000x^213+3600x^214+270x^216+1104x^217+1344x^218+48x^220+156x^221+144x^222+3x^224

The gray image is a linear code over GF(4) with n=272, k=8 and d=189.
This code was found by Heurico 1.16 in 358 seconds.