The generator matrix

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

generates a code of length 58 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+432x^166+351x^168+984x^170+234x^172+744x^174+141x^176+168x^178+180x^180+552x^182+87x^184+192x^186+18x^188+6x^192+6x^200

The gray image is a linear code over GF(4) with n=232, k=6 and d=166.
This code was found by Heurico 1.16 in 99 seconds.