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

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+912x^172+672x^174+2205x^176+936x^178+2511x^180+1104x^182+2385x^184+876x^186+1659x^188+588x^190+1314x^192+348x^194+720x^196+84x^198+54x^200+3x^204+6x^208+3x^212+3x^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 3.32 seconds.