The generator matrix

 1  0  1  1 X^2+X  1  1  1  0  1  1  X  1  1 X+2  1  1 X^2+2  0  1 X^2+X+2 X+2  1 X^2+X  2  1  1 X^2+2 X^2 X^2  2  1
 0  1  1 X^2+X  1 X+3 X^2+3 X^2  1  X X^2+X+3  1 X^2  1  1 X^2+X+1 X+2  1  1 X^2+X+1  1  1 X+2  1  1  3 X^2+X  X  1  1  1  0
 0  0  X  0  2 X^2 X^2+2 X+2 X^2+X+2  X X^2+X+2 X+2 X^2+X+2 X^2+X X^2+X  X X^2+X+2 X^2+X+2  2 X^2 X^2+X+2  0  0 X^2+2  X  2 X^2  X X^2+X+2  X X^2+X  2
 0  0  0  2  2  0  2  0  2  2  2  0  0  0  2  0  0  0  2  2  0  2  0  0  2  0  2  0  2  0  0  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+62x^28+302x^29+638x^30+764x^31+672x^32+766x^33+486x^34+254x^35+101x^36+20x^37+11x^38+6x^39+11x^40+1x^44+1x^46

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 0.109 seconds.