The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1  1  1  0 X+2  1  1  1  1  1  1  1  1  2  X  2  X  X  X  0  X  X  2  X  X  0  X  X  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  0 X+2 X+1  3  1  1  2  X X+3  1  2  X X+3  1  1  1  1  1  0 X+2  X  2  X  X  0 X+2  X  2  X  X  0  0  2  2 X+1 X+1 X+3 X+3 X+2 X+2  X  X  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  0  0

generates a code of length 73 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+13x^72+90x^73+12x^74+2x^76+4x^77+2x^78+2x^81+1x^82+1x^90

The gray image is a code over GF(2) with n=292, k=7 and d=144.
This code was found by Heurico 1.16 in 0.178 seconds.