The generator matrix

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

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+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 0.063 seconds.