The generator matrix

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

generates a code of length 58 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+180x^170+168x^171+18x^172+288x^174+192x^175+27x^176+72x^178+6x^180+12x^184+36x^186+24x^187

The gray image is a linear code over GF(4) with n=232, k=5 and d=170.
This code was found by Heurico 1.16 in 0.063 seconds.