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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+17x^66+81x^68+125x^70+64x^71+610x^72+384x^73+561x^74+64x^75+31x^76+45x^78+16x^80+10x^82+28x^84+10x^86+1x^136

The gray image is a code over GF(2) with n=584, k=11 and d=264.
This code was found by Heurico 1.16 in 20.2 seconds.