The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1 X+2  1  1  X  1  1  1  X  1  2  1  1  0  1  1  X  1  1 X+2  1  1 X+2  1  1 X+2 X+2  1  1  0  1  1  1  1  X  2  1  1  0  X  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  1  1  1  1
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+3  1 X+1 X+2  1 X+2 X+1  2  1  3  1 X+3  0  1  1 X+2  1  X X+3  1  X X+1  1  0  1  1  X  X X+1  1 X+2 X+1  2  3  1  1 X+2 X+3  X  2 X+3  2  X  0  2 X+2  0  X X+3  3 X+1  X  1  1  3  1  1 X+1 X+2  X  0  0
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X  1  X  0  3 X+3  0 X+1  3  0  2 X+3  X X+3  3 X+2 X+3  1 X+1  2  3  1 X+2 X+1  2  3  2  1 X+2 X+3  2  2  1 X+2 X+3  X  1  X  0  1  1  3  2  0  X  0 X+1  1  2 X+1 X+2  X  3 X+1  3  0 X+2 X+3  2 X+2 X+2 X+2  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+60x^76+114x^77+57x^78+130x^79+25x^80+46x^81+20x^82+22x^83+16x^84+8x^85+1x^86+9x^88+1x^96+1x^98+1x^106

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 0.174 seconds.