The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+156x^168+96x^169+264x^171+864x^172+252x^173+264x^175+555x^176+132x^177+48x^179+468x^180+156x^181+216x^184+108x^185+168x^187+270x^188+24x^189+24x^191+21x^192+3x^196+3x^208+3x^212

The gray image is a linear code over GF(4) with n=236, k=6 and d=168.
This code was found by Heurico 1.16 in 0.104 seconds.