The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) 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 2.3 seconds.