The generator matrix

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

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+183x^160+240x^161+192x^162+678x^164+732x^165+360x^166+1152x^168+936x^169+540x^170+1371x^172+1452x^173+720x^174+1926x^176+1344x^177+792x^178+1314x^180+1044x^181+360x^182+375x^184+360x^185+108x^186+39x^188+36x^189+45x^192+27x^196+21x^200+18x^204+9x^208+9x^212

The gray image is a linear code over GF(4) with n=232, k=7 and d=160.
This code was found by Heurico 1.16 in 1.72 seconds.