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

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+24x^74+66x^75+196x^76+280x^77+310x^78+396x^79+343x^80+192x^81+40x^82+50x^83+100x^84+40x^85+9x^86+1x^150

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 0.797 seconds.