The generator matrix

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

generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+21x^36+192x^39+36x^40+3x^48+3x^52

The gray image is a linear code over GF(4) with n=52, k=4 and d=36.
This code was found by Heurico 1.16 in -3.24e-008 seconds.