The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  2  1  X  1  2  X  1  X  0
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2 X^2+X X^2+X  X X^2 X+2  2  X X^2+X+2 X^2+2 X+2 X^2+2  X X^2  X X^2+X X^2+X+2  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2  X X+2  0 X^2+X X^2+X+2 X^2+2  X X+2  X  X X^2+X+2 X^2+X  X  2 X^2+X X^2+X+2 X^2 X^2+2  0 X^2+X+2  2
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  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+312x^28+128x^29+510x^30+256x^31+438x^32+128x^33+188x^34+76x^36+6x^38+4x^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 1.23 seconds.