The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+88x^76+176x^78+186x^80+16x^82+40x^84+3x^88+1x^104+1x^112

The gray image is a code over GF(2) with n=316, k=9 and d=152.
This code was found by Heurico 1.16 in 0.266 seconds.