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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+186x^172+9x^176+48x^180+6x^188+3x^192+3x^208

The gray image is a linear code over GF(4) with n=232, k=4 and d=172.
This code was found by Heurico 1.16 in 0.063 seconds.