The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2X+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 -6.48e-008 seconds.