The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X 2X+2 X+2  0 3X 2X 3X 2X+2  2 X+2 3X+2  0 3X  0 2X X+2 3X+2 2X+2 3X  X 3X+2 2X+2 2X+2  0  X
 0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X  0  0  0  0 2X  0  0 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  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+135x^28+592x^30+639x^32+544x^34+104x^36+16x^38+16x^40+1x^60

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 0.719 seconds.