The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a  0  X a^2*X+1 a^2*X+1
 0  0 a^2*X  0  X  0  X a*X a^2*X a^2*X a*X  0
 0  0  0  X a*X a*X  0 a*X  X a^2*X  0 a*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+123x^28+48x^30+387x^32+384x^33+288x^34+690x^36+1152x^37+432x^38+552x^40+27x^44+12x^48

The gray image is a linear code over GF(4) with n=48, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0107 seconds.