The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+96x^29+49x^30+176x^31+412x^32+160x^33+46x^34+64x^35+2x^36+1x^38+16x^39+1x^56

The gray image is a code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.032 seconds.