The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  0  X  0  1  X  0
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2 X^2+X+2 X^2+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X+2 X^2+X+2  X  2 X^2+X  X X^2+X X^2+X+2 X^2+X+2  X X^2  X X^2+2  X  X
 0  0 X^2+2  0  0 X^2+2 X^2 X^2 X^2 X^2  2  0 X^2+2  2 X^2  2 X^2+2 X^2+2  0  2  0  2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2  0
 0  0  0 X^2+2 X^2 X^2 X^2  2  0  0  2 X^2+2 X^2 X^2+2 X^2+2  0 X^2  2 X^2  0  2 X^2+2 X^2  2  0 X^2+2 X^2+2 X^2 X^2+2  0  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+351x^28+64x^29+400x^30+384x^31+531x^32+64x^33+176x^34+69x^36+7x^40+1x^48

The gray image is a code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 97.9 seconds.