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

generates a code of length 58 over F4[X,sigma]/(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 0.188 seconds.