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 X 1 1 X 1 1 X 1 1 1 X 1 1 X 1 X X 1 2 0 X X 1 X X 2 0 1 X 1 X 2 0 2 X X 2 X 2 0 1 2 X X X 2 2 0 1
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 2 0 2 2 0 2 0 2 2 0 0 2 2 0 0 2 2 2 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 0 2 2 2 0 0 0 2 0 0 2 2 0
generates a code of length 73 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.
Homogenous weight enumerator: w(x)=1x^0+8x^77+5x^78+1x^80+1x^82
The gray image is a code over GF(2) with n=292, k=4 and d=154.
This code was found by Heurico 1.16 in 0.176 seconds.