The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 X 1 1 X 1 1 1 X 1 X 1 X X 1 2 0 X X 1 X 1 2 0 X X 1 X 2 0 X 2 X 1 X 2 2 0 X 2 X 1 2 0 2 X X 2 X 2 0
0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 0 2 2 0 2 2 0 2 2 0 2 0 2 2 0 0 2 0 2 2 2 0 2 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 0 2 0 0 0 2 2
generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 89.
Homogenous weight enumerator: w(x)=1x^0+10x^89+2x^90+2x^91+1x^92
The gray image is a code over GF(2) with n=336, k=4 and d=178.
This code was found by Heurico 1.16 in 0.304 seconds.