The generator matrix

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

generates a code of length 12 over F4[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+33x^28+75x^32+822x^36+48x^40+33x^44+12x^48

The gray image is a linear code over GF(4) with n=48, k=5 and d=28.
This code was found by Heurico 1.16 in -3.24e-008 seconds.