The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1  1  1 2X+2 3X  1  1  1  1  1  1  0  0
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3 3X 2X+1  1  1  0 X+2 X+2  0  3  3  X  X
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X  0  0
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0  0 2X  0 2X  0  0 2X  0 2X
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 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+223x^28+1002x^30+1662x^32+1004x^34+181x^36+10x^38+7x^40+4x^44+2x^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 29.9 seconds.