The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+50x^76+96x^77+158x^78+92x^79+156x^80+96x^81+96x^82+36x^83+75x^84+28x^85+50x^86+16x^87+33x^88+20x^89+12x^90+3x^92+2x^104+4x^106

The gray image is a code over GF(2) with n=324, k=10 and d=152.
This code was found by Heurico 1.16 in 0.334 seconds.