The generator matrix

 1  0  0  1  1  1 a^2*X  1  1  0  1  1
 0  1  0  1  a a^2  1  X X+1  1 a^2*X a^2*X+1
 0  0  1 a^2  a  1  1 a*X+a a^2*X+1 X+a  1  a
 0  0  0  X  0  X a^2*X  0  X a*X a*X a^2*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+414x^28+576x^30+1539x^32+3456x^34+2892x^36+5184x^38+2268x^40+54x^44

The gray image is a linear code over GF(4) with n=48, k=7 and d=28.
This code was found by Heurico 1.16 in 0.094 seconds.