The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+108x^197+180x^200+624x^201+63x^204+3x^208+36x^213+9x^220

The gray image is a linear code over GF(4) with n=268, k=5 and d=197.
This code was found by Heurico 1.16 in 0.047 seconds.