The generator matrix

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

generates a code of length 15 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+180x^40+405x^44+435x^48+3x^60

The gray image is a linear code over GF(4) with n=60, k=5 and d=40.
This code was found by Heurico 1.16 in 6.87e-008 seconds.