The generator matrix

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

generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+84x^12+822x^16+1920x^18+3432x^20+11520x^22+25248x^24+17280x^26+5124x^28+105x^32

The gray image is a linear code over GF(4) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 0.416 seconds.