The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  X
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1 X+a a*X+a^2  1
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X  0 a*X a^2*X

generates a code of length 15 over F4[X]/(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 0.016 seconds.