The generator matrix

 1  0  0  1  1  1  2  1  1  0  1  1  X X^2+X+2  1  1  1 X^2 X^2+X+2 X+2  1 X^2+X  1  1  1  1  1  1 X^2+2 X^2+2  1  1
 0  1  0  0 X^2+3 X^2+3  1  2 X^2+1  1 X+2 X^2+X+1  1  1 X^2+X X+3 X^2+1  X X^2 X^2+X  0  1 X^2+X+2  3 X^2+2 X^2+X+3 X+3 X+3  1  1 X^2+X+3  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1 X^2+X+2  3  3 X^2+1 X+2  1 X^2 X^2+X X^2+X+3 X+2  1  1  1 X^2+1 X^2+X X^2+2 X+2 X^2+2  2  3  1 X^2+X+2 X^2+X+2  0  0
 0  0  0  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  2  2  2  2  2  2  2  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+163x^28+658x^29+1240x^30+1068x^31+2068x^32+1116x^33+1114x^34+428x^35+187x^36+106x^37+14x^38+16x^39+13x^40

The gray image is a code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 0.266 seconds.