The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+254x^72+64x^73+256x^74+64x^75+768x^76+64x^77+256x^78+64x^79+254x^80+1x^88+1x^104+1x^112

The gray image is a code over GF(2) with n=608, k=11 and d=288.
This code was found by Heurico 1.16 in 0.343 seconds.