The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+480x^178+342x^180+960x^182+324x^184+576x^186+102x^188+384x^190+39x^192+480x^194+168x^196+192x^198+36x^200+6x^204+6x^212

The gray image is a linear code over GF(4) with n=248, k=6 and d=178.
This code was found by Heurico 1.16 in 8.36 seconds.