The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+65x^28+158x^29+360x^30+238x^31+450x^32+234x^33+331x^34+120x^35+55x^36+6x^37+11x^38+10x^39+5x^40+2x^41+1x^42+1x^46

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 0.047 seconds.