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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+166x^75+102x^76+186x^77+293x^78+588x^79+283x^80+196x^81+62x^82+110x^83+22x^84+34x^85+4x^86+1x^150

The gray image is a code over GF(2) with n=632, k=11 and d=300.
This code was found by Heurico 1.16 in 0.594 seconds.