The generator matrix

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

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+338x^76+410x^78+431x^80+312x^82+228x^84+130x^86+114x^88+36x^90+24x^92+8x^94+2x^96+14x^100

The gray image is a code over GF(2) with n=324, k=11 and d=152.
This code was found by Heurico 1.11 in 76.7 seconds.