The generator matrix

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

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+53x^28+164x^29+187x^30+218x^31+184x^32+160x^33+51x^34+2x^35+2x^36+1x^38+1x^54

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.