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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+203x^76+20x^77+76x^78+108x^79+189x^80+244x^81+66x^82+300x^83+156x^84+220x^85+50x^86+100x^87+118x^88+28x^89+42x^90+4x^91+72x^92+18x^94+28x^96+4x^98+1x^140

The gray image is a code over GF(2) with n=332, k=11 and d=152.
This code was found by Heurico 1.16 in 3.79 seconds.