The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1 X+2  1  0  2  1  1  1  X  2  1  1  1  1  X  1  0  X  1  1  1  1  1 X+2  1  2  0  1  2  1  1  2  0  1 X+2  1  1  X  1  0  0  X  1  0  1  1  1  2  X X+2 X+2  1  1 X+2  2  1  1  1  1  1  0  0  1  1  1  0  1  0 X+2 X+2
 0  1  0  0  1 X+1  1  0 X+2  2  3  1 X+3  1  2  0  2  1  1  1 X+1  X  3 X+1  1  X X+2  1 X+3  1 X+3  X  X  1  3  1  0 X+2  1  0 X+1  1  1  2  X  2 X+3  1 X+3 X+2  1  1  1  0  3  3 X+2  1  X  1  1  1  3  2  1  1 X+2  X X+1 X+3  1  0 X+2  0  X  1  1  X  0  0
 0  0  1  1  1  2  3  1  3  X X+2  X  3 X+1  1  2  1  3 X+2 X+3  0  1  1  1  3  2  1  0 X+2  0 X+1 X+1 X+2  0  X  3  1 X+3  X  2  X  3 X+1 X+2  1 X+3 X+3  X  1  1 X+1  0  3  1  2  0 X+1  0  1 X+3  1 X+2  0  1  2 X+2  1  1 X+3 X+3  X  1 X+2  X X+1 X+3  2  0  1  1
 0  0  0  X X+2  0 X+2 X+2 X+2  0  0  0  X X+2  X X+2  0  2 X+2  2  X  0  X X+2  0  X  2  X  X  2  2  X  2  0  X  0  2  0 X+2  X  2  X  X  X  2  X  X  0  2  X  0  X  2  X  X  X X+2  X  X X+2  0  2  2 X+2  2 X+2  0  2  X  0  X  2  0  0  2  2 X+2 X+2  0  2
 0  0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  2  0  2  2  0  2  0  0  2  0  0  2  0  2  2  0  2  0  2  2  0  0  2  0  0  2  0  0  0  0  0  2  2  2  0  0  0  0  2  0  2  2  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+409x^74+671x^76+905x^78+662x^80+527x^82+348x^84+253x^86+164x^88+92x^90+41x^92+18x^94+1x^96+4x^98

The gray image is a code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.16 in 14.6 seconds.