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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+90x^160+300x^164+426x^168+48x^171+441x^172+576x^175+378x^176+2592x^179+405x^180+5184x^183+366x^184+3888x^187+375x^188+345x^192+327x^196+282x^200+189x^204+90x^208+69x^212+6x^216+3x^220+3x^228

The gray image is a linear code over GF(4) with n=244, k=7 and d=160.
This code was found by Heurico 1.16 in 2.72 seconds.