The generator matrix

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

generates a code of length 26 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+6x^76+72x^77+144x^78+24x^81+9x^88

The gray image is a linear code over GF(4) with n=104, k=4 and d=76.
As d=76 is an upper bound for linear (104,4,4)-codes, this code is optimal over F4[X,sigma]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in -3.24e-008 seconds.