The generator matrix

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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+416x^76+240x^77+382x^78+112x^79+333x^80+208x^81+236x^82+16x^83+76x^84+14x^86+8x^88+4x^92+1x^108+1x^116

The gray image is a code over GF(2) with n=632, k=11 and d=304.
This code was found by Heurico 1.16 in 0.454 seconds.