The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+466x^72+144x^74+176x^76+162x^80+48x^82+16x^84+10x^88+1x^96

The gray image is a code over GF(2) with n=300, k=10 and d=144.
This code was found by Heurico 1.11 in 5.22 seconds.