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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+16x^92+8x^93+5x^94+1x^96+1x^98

The gray image is a code over GF(2) with n=720, k=5 and d=368.
This code was found by Heurico 1.16 in 0.5 seconds.