The generator matrix

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

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+16x^26+23x^28+21x^30+96x^31+786x^32+11x^34+32x^35+13x^36+15x^38+9x^40+1x^58

The gray image is a code over GF(2) with n=256, k=10 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.