The generator matrix

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

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+48x^67+42x^68+96x^69+48x^71+12x^72+6x^76+3x^80

The gray image is a linear code over GF(4) with n=92, k=4 and d=67.
This code was found by Heurico 1.16 in 0.046 seconds.