The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 X 1
0 2X 0 0 0 0 0 2X 0 0 0 2X 2X 0 2X 2X 0 2X 0 0 0 2X 0 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0
0 0 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 0 0 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 2X 0
0 0 0 2X 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 0 0 0
0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 0
0 0 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 2X 0 0 2X 2X 0 0 0 2X 2X 0 2X 0 2X 0
0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 0 2X 2X 2X 0 0 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 0
generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+41x^32+21x^34+32x^35+144x^36+576x^37+144x^38+32x^39+16x^42+6x^48+10x^50+1x^66
The gray image is a code over GF(2) with n=296, k=10 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.