The generator matrix

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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+113x^76+240x^77+630x^78+384x^79+617x^80+408x^81+544x^82+224x^83+490x^84+208x^85+76x^86+64x^87+65x^88+8x^89+10x^90+8x^92+2x^94+2x^98+1x^112+1x^116

The gray image is a code over GF(2) with n=648, k=12 and d=304.
This code was found by Heurico 1.16 in 0.86 seconds.