The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0 X^2  1  1  1  1 X^2+X+2  X X+2  1  1  1  1  X X^2+X+2 X+2  1 X^2  1  1  1 X^2+X  1  2  X X^2+X+2  0  1  1 X^2+2  1  1  1 X^2+X+2  1  X  1  1  1  1 X^2+X+2  1  1 X+2  1 X^2 X^2+2  1  1  2 X^2+X  1  X X^2+2  0 X^2+2  1 X^2+2  1  1  1  X  0  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1  X X+2  X X^2+X+3 X^2+X+1 X^2+2  1  1 X+3 X^2+X+2 X+1 X^2+X X^2+X  1  1  X X^2 X+2  3 X+3  1  X  1  1  X  1  2 X^2+X+1 X^2+X+2  0 X+1 X^2+X+1  1 X+2 X^2  1 X^2+X+2  2 X^2+X+2  1 X^2 X^2+2  1 X^2+X+2  1  1  3 X^2+X  1 X^2+X+2  0  1  1  X  1 X^2+X+2  1  1 X^2  3  2  1 X^2
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X+2 X^2+3 X+1  X  1 X^2+X+1  X  2 X+3  1 X^2  1 X+1  0  1  1 X^2+X X^2+1 X^2+2 X^2+X+2 X+3 X^2+2 X^2+1  1 X^2+1 X^2 X^2+X+1  1 X^2+X+3 X^2+X+2  1 X^2  0  1 X^2+X  2 X+2 X+1 X^2+1 X^2+X+1 X^2+X+2 X^2+X+2 X+2 X+2 X+3 X^2+X+1  1 X+3  1  3 X+3 X^2+X+1  1 X^2 X^2+1  3  0  2 X+2  1 X^2 X^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+142x^72+640x^73+662x^74+694x^75+532x^76+380x^77+286x^78+254x^79+159x^80+136x^81+64x^82+72x^83+33x^84+32x^85+3x^86+4x^88+1x^90+1x^96

The gray image is a code over GF(2) with n=608, k=12 and d=288.
This code was found by Heurico 1.16 in 0.328 seconds.