The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+123x^32+4x^40

The gray image is a code over GF(2) with n=256, k=7 and d=128.
This code was found by Heurico 1.16 in 0.016 seconds.