The generator matrix

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

generates a code of length 12 over F4[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+15x^32+225x^36+9x^40+3x^44+3x^48

The gray image is a linear code over GF(4) with n=48, k=4 and d=32.
This code was found by Heurico 1.16 in 1.01e-007 seconds.