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  0  1  1  1  1  1  1  1  1  2  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  1  1  1  1  X  0  X X^2  0  X X^2+2  X  1
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  X  0  0  2 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2  2 X^2+X  X  2 X^2+2 X+2 X^2+X+2 X^2+2  2 X^2+X+2 X+2  2 X^2+2 X+2 X^2+X+2 X^2+2  2 X^2+X+2 X+2  2  2 X+2 X^2+X+2 X^2+2 X^2+X+2 X+2 X^2+2 X^2+X+2 X^2+X+2  2  2 X^2+2 X^2+2 X+2 X+2  X  X X^2+X+2  X  X X^2+X  X  X  0
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 X+2 X^2+2  2 X^2+X+2 X+2 X^2+2 X+2 X^2  X X^2+X+2  0 X^2+2 X^2+X X^2+X X^2  0  X  X  X  2  2 X+2 X+2  2 X^2 X^2+X X^2+X+2 X^2+2 X^2 X^2+X X^2+X X^2  2 X+2  X  0  0 X^2+X+2  X  0  0 X+2 X^2  X X^2+2 X^2+X X^2+2  X X^2+2 X^2+X+2 X^2+X+2  2  X  0 X+2  X X^2+2  0 X^2+X X^2  0

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+30x^72+180x^73+158x^74+288x^75+160x^76+168x^77+32x^78+1x^80+4x^81+1x^82+1x^130

The gray image is a code over GF(2) with n=600, k=10 and d=288.
This code was found by Heurico 1.16 in 0.282 seconds.