The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+1167x^172+3261x^176+3168x^180+3366x^184+2697x^188+1875x^192+741x^196+96x^200+3x^208+3x^212+6x^216

The gray image is a linear code over GF(4) with n=244, k=7 and d=172.
This code was found by Heurico 1.16 in 2.21 seconds.