The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  X  1  1 X^2+2  1  0  1  X  1  1  X  1  X X^2
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+X  X  X X^2+X X^2+X+2 X^2+2 X^2+2  X  2  X  X X+2 X^2 X^2+X+2 X^2  X  X  X
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2 X^2+X X^2  X  X X^2+X+2 X+2 X^2 X^2+2 X^2+X+2 X^2+2 X^2+X X^2  X  0  0  2  2
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0  0  0  2 X^2  2 X^2 X^2+2 X^2+2  2  2  0 X^2  0  0 X^2  2 X^2 X^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+208x^27+294x^28+482x^29+610x^30+946x^31+666x^32+502x^33+146x^34+108x^35+60x^36+54x^37+11x^38+2x^39+3x^40+2x^41+1x^46

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 53.8 seconds.