The generator matrix

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

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+61x^28+94x^29+188x^30+372x^31+168x^32+62x^33+50x^34+16x^35+10x^36+1x^38+1x^58

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.