The generator matrix

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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+162x^164+219x^168+192x^171+126x^172+1152x^175+114x^176+1728x^179+111x^180+90x^184+54x^188+33x^192+36x^196+30x^200+18x^204+6x^208+18x^212+3x^216+3x^228

The gray image is a linear code over GF(4) with n=236, k=6 and d=164.
This code was found by Heurico 1.16 in 2.04 seconds.