The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  X  1  1  2  1  1 X+2  1  0  X  1  1  1  X  1  2  0  1  1  1  1  1  1  1  2  0  1  1  0 X+2  1  1  1  1  1  2  1  1 X+2  1  X  1  1  1  2  1  2  1  0 X+2  1  X  1  1  1  0  X  1  2  1 X+2  0  1  0  X  0  1  0  1  X  X
 0  1  0  0  3 X+1  1  2  2 X+3  1  2  1  1  0  3  1 X+1  1  2 X+2  2  1  1 X+3  1  0  X  X  0  2  2 X+2  2  2  2 X+2  X  1  1  3  1  0  2 X+1  1 X+1 X+2  0 X+3  1  X  0 X+3  X X+3  1 X+2  1  1 X+2  1 X+2 X+1  X  0 X+2  3  1  2  1  X  1  1  X X+2  X  0 X+2  1 X+2
 0  0  1  1  3  2  3  1  0 X+1  0 X+3  2  1  2  1  1  0  2  1  3  2  0  2 X+3  3  1 X+3  1 X+3 X+2 X+2 X+1  1  1  1  1  1  X X+1 X+2 X+3 X+2  1  X X+3  1 X+3  1 X+2  X X+1 X+3  3  1 X+3  0  X X+1  0 X+2  X  2  3  3  0  1 X+3 X+1  X X+1  X  2  3 X+2  1  1  1  2  2  1
 0  0  0  X  X  0  X  X  X  0  X  0  X  0  2 X+2 X+2  2  2 X+2 X+2 X+2 X+2 X+2  2  2  2  0  0 X+2  X X+2 X+2  2 X+2  X  2  X X+2  2  2  2  0  0  0 X+2 X+2  X  0 X+2  2  2  X  0  0 X+2 X+2  2  0  2  X  0  2  2  X  X  X X+2  2  2  0  X  2  X X+2  X  2  X  X  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+301x^76+482x^78+387x^80+348x^82+218x^84+124x^86+66x^88+52x^90+45x^92+10x^94+2x^96+8x^98+4x^100

The gray image is a code over GF(2) with n=324, k=11 and d=152.
This code was found by Heurico 1.16 in 3.38 seconds.