The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+96x^71+440x^72+774x^73+1108x^74+1458x^75+1889x^76+2160x^77+2264x^78+2472x^79+2465x^80+2746x^81+2662x^82+2348x^83+2390x^84+2008x^85+1639x^86+1322x^87+910x^88+678x^89+429x^90+258x^91+121x^92+48x^93+51x^94+12x^95+8x^96+2x^97+5x^98+2x^102+2x^103

The gray image is a code over GF(2) with n=324, k=15 and d=142.
This code was found by Heurico 1.13 in 20.3 seconds.