The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^2+2  1 X+2  1  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1  X  1  1  0 X^2+2
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3  3 X^2+2  1 X+2  1 X^2+1 X+1  0  1 X^2+X+3 X^2+X  1 X^2+1 X^2+X+3  3  0 X+2 X^2+2 X^2+X  0  2 X+2  X  X
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  0  0  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  2  0  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+283x^28+128x^29+464x^30+256x^31+551x^32+128x^33+208x^34+27x^36+1x^44+1x^52

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 1.16 seconds.