The generator matrix

 1  0  0  1  1  1  2  1  1  1  X  1 X^2+X X^2+X  1  1 X^2+X+2 X^2  0  1  1  1  1  1  X X+2  2  1 X^2  X  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+X X+3  1 X^2+X+1 X^2+2  1  X X^2+X+1  X  1  1 X+1 X^2+3 X+2 X^2+X+2  0  1  1  1  1  1 X^2+2 X^2+3
 0  0  1 X+3 X+1  2 X^2+X+1  X X^2+1 X^2+2 X^2+2  3  1 X+3 X^2+X+1 X^2+X+3  1 X^2+1 X^2+X+2 X^2+X  X X^2+X+2  2  3 X+2  1 X^2+2  1 X^2+X+3  1 X^2+X+1

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+248x^28+800x^29+744x^30+874x^31+460x^32+536x^33+239x^34+114x^35+67x^36+12x^37+1x^38

The gray image is a code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 0.062 seconds.