The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+22x^26+28x^27+52x^28+76x^29+111x^30+664x^31+155x^32+664x^33+104x^34+76x^35+40x^36+28x^37+15x^38+4x^40+2x^42+4x^44+1x^46+1x^54

The gray image is a code over GF(2) with n=256, k=11 and d=104.
This code was found by Heurico 1.16 in 0.062 seconds.