The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  1 X^2  1  1  1 X^2  X  X  X
 0 X^2+2  0  0  0 X^2 X^2+2 X^2  0  2 X^2+2 X^2+2  0  2 X^2+2 X^2+2  0 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2  2  2 X^2  2 X^2 X^2+2 X^2  0  0
 0  0 X^2+2  0 X^2 X^2 X^2  2  0  2 X^2 X^2+2 X^2 X^2  2  2 X^2 X^2 X^2+2 X^2 X^2  0 X^2+2  0 X^2+2  0 X^2  0  2 X^2  0 X^2
 0  0  0 X^2+2 X^2  2 X^2+2 X^2+2  0 X^2+2  2 X^2+2 X^2  0 X^2+2  0 X^2+2 X^2 X^2 X^2+2 X^2  2  0 X^2+2 X^2+2 X^2 X^2+2 X^2+2  2  0 X^2+2 X^2
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  0  0  0  2  0  0  2  0  0  2  2  0  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+200x^28+224x^30+256x^31+720x^32+256x^33+224x^34+128x^36+38x^40+1x^48

The gray image is a code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 1.86 seconds.