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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+372x^197+696x^198+117x^200+540x^201+732x^202+69x^204+204x^205+396x^206+27x^208+132x^209+204x^210+12x^212+168x^213+108x^214+15x^216+48x^217+120x^218+12x^220+72x^221+48x^222+3x^236

The gray image is a linear code over GF(4) with n=272, k=6 and d=197.
This code was found by Heurico 1.16 in 19.5 seconds.