The generator matrix

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

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+204x^166+192x^167+384x^168+348x^169+468x^170+264x^171+213x^172+108x^173+360x^174+84x^175+123x^176+180x^177+240x^178+72x^179+120x^180+48x^181+180x^182+84x^183+156x^184+72x^185+60x^186+72x^187+27x^188+12x^189+24x^190

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 0.063 seconds.