The generator matrix

 1  0  1  1  1 X^2+X+2  1  1 X^2+2  1 X^2+X  1  1 X^2+X+2  1  2  1  1  1  1  2 X^2  1  1 X+2 X^2 X^2+X+2  1  2 X+2  1  X
 0  1 X+1 X^2+X+2 X^2+1  1 X+3 X^2+2  1 X^2+X  1 X^2+1  2  1 X+1  1 X^2+3 X^2+X+2 X^2+X+3  1  1  1 X^2+X X^2+X  1  X  1  X  1  1  2 X^2+X+2
 0  0 X^2  0  0  2  0  2  2 X^2+2 X^2+2 X^2+2 X^2 X^2+2  0 X^2+2 X^2 X^2+2 X^2  2  2 X^2  0 X^2  2 X^2+2  0 X^2+2  0  2  0  0
 0  0  0 X^2+2  2 X^2 X^2  0  0 X^2 X^2 X^2+2  2  2  2  2  0  2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2+2  0  0  0  2  2  2 X^2 X^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+133x^28+272x^29+534x^30+752x^31+775x^32+752x^33+456x^34+272x^35+106x^36+32x^38+8x^40+1x^44+2x^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.