The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+18x^74+166x^75+241x^76+242x^77+249x^78+188x^79+196x^80+150x^81+113x^82+106x^83+59x^84+62x^85+50x^86+52x^87+64x^88+36x^89+23x^90+12x^91+4x^92+4x^93+3x^94+4x^95+2x^96+2x^97+1x^104

The gray image is a code over GF(2) with n=320, k=11 and d=148.
This code was found by Heurico 1.16 in 0.462 seconds.