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

generates a code of length 58 over F4[X]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+93x^160+192x^164+417x^168+1272x^172+1827x^176+60x^180+60x^184+45x^188+27x^192+45x^196+27x^200+15x^204+9x^208+3x^212+3x^224

The gray image is a linear code over GF(4) with n=232, k=6 and d=160.
This code was found by Heurico 1.16 in 0.187 seconds.