The generator matrix

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

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+680x^28+984x^29+2146x^30+2632x^31+3637x^32+2584x^33+2092x^34+920x^35+584x^36+48x^37+50x^38+22x^40+4x^44

The gray image is a code over GF(2) with n=256, k=14 and d=112.
This code was found by Heurico 1.16 in 76.4 seconds.