The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1  X  1  1  1  1 X^2+2 X^2+2 X^2  X  X
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+X  2  0  0 X^2+X  X X^2 X^2+X X^2+2 X^2  X X^2+X+2  X  2 X^2 X^2+X+2 X+2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X+2 X^2+X X^2 X^2+X X^2+X  0 X^2+2 X+2 X^2+X+2 X^2+2  2 X^2+2  X  2  X  0  X X^2+X+2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  2  2  2  0  0  2  0  0  2  2  2  0  2  2
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  0  0  0  2  0  0  2  2  2  2  0  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+347x^28+48x^29+704x^30+464x^31+1163x^32+208x^33+776x^34+48x^35+265x^36+56x^38+15x^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 4.17 seconds.