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  2  1  1  1  2  X  X  X
 0 2X+2  0  0  0  2 2X+2  2  0 2X 2X+2 2X+2  0 2X 2X+2 2X+2  0 2X+2 2X+2 2X+2  2  2  2 2X 2X  2 2X  2 2X+2  2  0  0
 0  0 2X+2  0  2  2  2 2X  0 2X  2 2X+2  2  2 2X 2X  2  2 2X+2  2  2  0 2X+2  0 2X+2  0  2  0 2X  2  0  2
 0  0  0 2X+2  2 2X 2X+2 2X+2  0 2X+2 2X 2X+2  2  0 2X+2  0 2X+2  2  2 2X+2  2 2X  0 2X+2 2X+2  2 2X+2 2X+2 2X  0 2X+2  2
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0  0 2X  0  0 2X  0  0 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+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 1.88 seconds.