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

generates a code of length 59 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+198x^156+369x^160+408x^164+48x^165+432x^168+576x^169+423x^172+2592x^173+438x^176+5184x^177+396x^180+3888x^181+372x^184+279x^188+291x^192+222x^196+153x^200+69x^204+21x^208+18x^212+3x^216+3x^220

The gray image is a linear code over GF(4) with n=236, k=7 and d=156.
This code was found by Heurico 1.16 in 2.65 seconds.