The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+42x^28+153x^30+128x^31+408x^32+128x^33+122x^34+16x^36+13x^38+12x^40+1x^56

The gray image is a code over GF(2) with n=256, k=10 and d=112.
This code was found by Heurico 1.16 in 0.032 seconds.