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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+40x^74+72x^75+226x^76+272x^77+324x^78+408x^79+151x^80+248x^81+60x^82+96x^83+76x^84+56x^85+16x^86+1x^88+1x^144

The gray image is a code over GF(2) with n=632, k=11 and d=296.
This code was found by Heurico 1.16 in 0.594 seconds.