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

generates a code of length 72 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+138x^68+192x^69+352x^70+192x^71+486x^72+192x^73+160x^74+64x^75+78x^76+128x^77+64x^78+1x^128

The gray image is a code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.453 seconds.