The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+110x^28+64x^29+88x^30+95x^32+64x^33+64x^34+16x^36+8x^38+2x^44

The gray image is a code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.16 in 0.0158 seconds.