The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+266x^28+88x^29+782x^30+408x^31+1140x^32+456x^33+516x^34+72x^35+306x^36+46x^38+14x^40+1x^48

The gray image is a code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 3.84 seconds.