The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  X  X  1  1  1  1  0  1  1 X+2  1  1  1  1  1  1  0  1  1  X  0  1  1 X+2  1  1  1  1  1  1  1  1  0 X+2  2 X+2  1  X  1  1  X  1  0  2  2  2  2  X X+2  X  X  X  2  2  1  1  0  1  1  1  1  X  1  1  1  1  0
 0  1  1 X+2 X+1  1  3  2  1  X X+3  1  1  1  0  1 X+2  2  1 X+3  X  1  1 X+3 X+3  1 X+1  0  1  3  X  1  1  0 X+2  1 X+3  1 X+3  0  1 X+2  2 X+2  1  1  1  1 X+1 X+2 X+1  0  2  X  1  1  1  1  1  1  1  1  1  1  1  1  3 X+1  1  X X+3  X  2  2  0  3 X+1 X+2  0
 0  0  X  0  2  0  2  X  X  X  X X+2  0  X  0 X+2 X+2 X+2  0  2  0 X+2  2 X+2  X  X  0 X+2 X+2  0 X+2 X+2  X  X  X  X X+2 X+2  0  2  0  2  2  2  2  2  2  2 X+2  0 X+2  2  2  0  2  2  0  0  X  X  0  2  2  0  X X+2  X  0  X X+2  2  X  2  X X+2  0  X  0  X
 0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  0  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  2  2  2  2  2  0  0  0  2  2  0  2  0  2  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+76x^76+72x^77+98x^78+68x^79+77x^80+36x^81+50x^82+12x^83+9x^84+4x^85+2x^86+2x^90+1x^92+2x^96+2x^104

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 0.339 seconds.