The generator matrix

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

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+225x^32+576x^36+216x^40+6x^48

The gray image is a linear code over GF(4) with n=48, k=5 and d=32.
This code was found by Heurico 1.16 in 0.156 seconds.