The generator matrix

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

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+99x^40+90x^44+768x^45+15x^48+45x^56+6x^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 0.078 seconds.