The generator matrix

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

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+185x^28+48x^29+464x^31+679x^32+464x^33+48x^35+131x^36+24x^40+3x^44+1x^52

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 7.02 seconds.