The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+192x^169+228x^170+336x^171+255x^172+576x^173+288x^174+252x^175+276x^176+144x^177+156x^178+144x^179+156x^180+120x^181+132x^182+72x^183+111x^184+156x^185+96x^186+96x^187+6x^188+96x^189+60x^190+60x^191+24x^192+60x^193+3x^196

The gray image is a linear code over GF(4) with n=236, k=6 and d=169.
This code was found by Heurico 1.16 in 0.079 seconds.