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  X  1  1  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  X a*X  0 a^2*X a*X  X a*X  0  X  0 a^2*X a*X  X a^2*X a*X  0 a*X a*X  0  X  0 a*X  X a*X a*X a*X  0  0  X  X  X a*X  X a^2*X  0  X a^2*X a*X a*X  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X a^2*X a^2*X  0  X a^2*X  0 a^2*X  0 a*X a*X a*X a*X a^2*X  0 a^2*X  X  0 a*X a^2*X a^2*X  X  0 a*X  0 a*X a^2*X a*X  0 a*X  X  X  X a*X  0 a*X  X a^2*X  X  0
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  X  X a^2*X a^2*X a^2*X a*X  0 a^2*X a^2*X  0  X a*X  0 a^2*X  0 a*X  X  0 a*X  X a*X  0 a*X a*X a*X  X  X a*X a*X a*X  X a*X  X a^2*X a*X a^2*X  X  X a^2*X  X a*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X  X a*X a^2*X a^2*X a*X  0 a*X  X a*X a*X  0  0 a^2*X a^2*X a^2*X a*X  X a*X  0 a*X a*X a*X a^2*X a^2*X a^2*X  0  X  0  0  X a^2*X a^2*X  0 a^2*X a*X  X a*X  X  0 a^2*X a^2*X

generates a code of length 57 over F4[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+81x^156+150x^160+210x^164+192x^165+150x^168+1152x^169+108x^172+1728x^173+69x^176+78x^180+33x^184+42x^188+24x^192+48x^196+21x^200+6x^204+3x^220

The gray image is a linear code over GF(4) with n=228, k=6 and d=156.
This code was found by Heurico 1.16 in 0.182 seconds.