The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+104x^73+263x^74+520x^75+429x^76+710x^77+580x^78+748x^79+624x^80+744x^81+534x^82+594x^83+495x^84+534x^85+324x^86+352x^87+209x^88+174x^89+73x^90+72x^91+26x^92+36x^93+12x^94+12x^95+6x^96+2x^97+6x^98+6x^99+2x^100

The gray image is a code over GF(2) with n=324, k=13 and d=146.
This code was found by Heurico 1.16 in 4.85 seconds.