The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 179.

Homogenous weight enumerator: w(x)=1x^0+720x^179+282x^180+936x^183+336x^184+600x^187+144x^188+324x^191+144x^192+252x^195+75x^196+180x^199+36x^200+60x^203+3x^208+3x^212

The gray image is a linear code over GF(4) with n=248, k=6 and d=179.
This code was found by Heurico 1.16 in 0.156 seconds.