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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+19x^68+13x^70+64x^71+31x^72+768x^73+31x^74+64x^75+13x^76+18x^78+1x^82+1x^142

The gray image is a code over GF(2) with n=584, k=10 and d=272.
This code was found by Heurico 1.16 in 0.406 seconds.