The generator matrix

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

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+144x^28+192x^29+640x^30+576x^31+1028x^32+576x^33+592x^34+192x^35+128x^36+16x^38+10x^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 0.125 seconds.