The generator matrix

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

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+66x^27+326x^28+600x^29+784x^30+734x^31+677x^32+468x^33+264x^34+86x^35+52x^36+28x^37+6x^38+2x^39+2x^42

The gray image is a code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 0.094 seconds.