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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+104x^76+96x^78+37x^80+6x^84+1x^88+10x^92+1x^104

The gray image is a code over GF(2) with n=312, k=8 and d=152.
This code was found by Heurico 1.16 in 0.312 seconds.