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  1  1  1  X  0  X  X  1  1  X  2  0  0  2  0 X^2
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  0 X^2+2  X X^2+X+2  X  0  2 X+2 X^2  0 X^2+X X+2 X^2 X^2+X+2 X^2+X  0 X^2  X X+2  0  2  X  0  X X^2+X+2 X^2 X^2+2  2  X X^2+X+2  2 X+2 X^2 X^2+2 X^2+X X^2+X+2 X^2+2 X^2 X^2+X+2 X^2+X X^2+2 X^2  0  2 X^2+X X^2+X+2 X+2  X  0  0  2  2 X^2 X^2+2 X+2 X+2 X^2+2 X^2  0  X  X  X  X
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X^2+X+2 X+2 X^2  0 X+2  X X^2 X^2+X+2  X X^2+2 X^2+2 X^2 X^2+X X^2+X+2  2 X^2+X X+2  2  2  2 X+2 X^2  X X^2 X^2 X+2 X^2+X+2 X^2+2  X  X  2 X^2+X X^2 X^2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2  X  X X^2+X X^2+X X^2+X+2 X^2+X+2  0  0  2  2  0  2 X^2+X+2  X  X  X X^2+X X^2+X+2 X+2  X X^2  0  2 X^2+X  X
 0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  2  0  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  2  2  2  0  0  2  0  2  2  2  0  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+355x^74+272x^75+329x^76+384x^77+383x^78+736x^79+272x^80+384x^81+409x^82+272x^83+219x^84+69x^86+10x^88+1x^136

The gray image is a code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 4.41 seconds.