The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 1 X 2X X 2X+2 X 2 X X X X 1 1 1 1
0 X 2X+2 X+2 2X 3X+2 2 3X 0 X+2 2X+2 3X X+2 X 2X 3X+2 2 X 3X X 3X+2 X X X 0 2X 2X+2 2 0 2X 2X+2 2
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+121x^32+4x^36+2x^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.