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

generates a code of length 79 over Z4[X]/(X^2+2) 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 0.609 seconds.