The generator matrix

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

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+558x^40+720x^42+1080x^44+1305x^48+432x^50

The gray image is a linear code over GF(4) with n=60, k=6 and d=40.
This code was found by Heurico 1.16 in 0.171 seconds.