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

generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+933x^224+1416x^228+732x^232+312x^236+360x^240+132x^244+192x^248+12x^252+6x^272

The gray image is a linear code over GF(4) with n=308, k=6 and d=224.
This code was found by Heurico 1.16 in 0.141 seconds.