The generator matrix

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

generates a code of length 12 over F4[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+576x^31+225x^32+1152x^35+576x^36+1344x^39+216x^40+6x^48

The gray image is a linear code over GF(4) with n=48, k=6 and d=31.
This code was found by Heurico 1.16 in 6.97 seconds.