The generator matrix

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

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+333x^40+576x^41+408x^42+672x^44+384x^45+144x^46+783x^48+576x^49+216x^50+3x^56

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 0.015 seconds.