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 a*X a^2*X  X a*X  X  X a*X a^2*X  X a*X a^2*X  X  0 a^2*X  X  0  0 a^2*X a*X  X  X a*X  X  X a^2*X  X  0  X a^2*X  0  X  X a^2*X a*X  X  0  X  X a^2*X a*X  X  X  0 a^2*X a^2*X  0 a^2*X a^2*X
 0  0  X  0  0  0  0  X  X  X a*X  0 a*X a^2*X a^2*X  0 a*X  0  0 a*X  X  X  X  X a*X a*X a^2*X  X  X a^2*X a^2*X a^2*X  X a^2*X  0  X a*X  X a^2*X  0 a*X a^2*X a*X a^2*X  X a*X  X  0 a^2*X  X  0 a*X  0 a*X  0 a*X  0  X a*X
 0  0  0  X  0  0  X a^2*X a*X a*X a*X a*X  0  X  X a^2*X  X a^2*X a*X a*X a^2*X a*X  0  0 a*X a*X  0 a*X a*X  X  0 a*X a^2*X  X a*X  0 a^2*X a*X a*X  X a^2*X  0  0  0  0  X a^2*X  X a^2*X a^2*X  X  X  X  X  0  0  X  0 a*X
 0  0  0  0  X  0 a^2*X  0  X a*X a^2*X a*X a^2*X a^2*X  0  X  X  0  X  0 a^2*X a*X a^2*X a^2*X  X  X a^2*X a*X  0 a*X  0  0  0  0 a*X  0  X a^2*X  X a^2*X  0 a^2*X a*X  X a^2*X a*X  0  X  0 a*X  X  0 a^2*X a*X a^2*X a*X a*X  X a^2*X
 0  0  0  0  0  X  X  X a^2*X  X  X  0 a^2*X a^2*X  X  X a*X a^2*X  X  X a*X a^2*X  0 a*X  0  0 a^2*X a*X a^2*X  X  X a^2*X a^2*X  X a^2*X a^2*X a*X  X  X  0  X  0 a^2*X a^2*X a^2*X  X a*X  X a*X a^2*X  0 a^2*X  X a*X a*X  0 a*X a^2*X a*X

generates a code of length 59 over F4[X]/(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 2.62 seconds.