The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1  X  1  X  1  X  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  X  X  1  2  1  1  2  2  2  1  1  1  2  X  1  X  X  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  0  0  2  2  2  0  2  2  2  0  2  2  2  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  2  0  2  0  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0  0  2  0  2  2  2  0  2  0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  0  0  0  0  2  0  0  2  2  2  0  2  0  0  2  0  2  0  0  2  2
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0  0  2  0  0  0  2  2  0  0  2  2  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  0  0  0  2  2  0  0  2  0  0  0  2  0  2  2  2  2  0  2  2  0  2  2  2  0  0  2  0  2  0  0  2  2  0  0  0  0  0  2  0  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  0  2  2  0  2  0  2  2  2  0  2  0  0  0  2  0  2  0  0  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  0  2  2  0  2  2  2  0  0  2  0  0  2  0  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  2  0  2  2  2  0  2  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  2  2  0  0  2  0  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  2  2  2  0  2  2  2  0  0  0  2  0  0  2  0  2  0  2  2  0  0  0  2  0  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  2  2  0  2  0  2  2  2  0  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  0  0  0  0  2  2  0  0  0  2  0  2  0  0  0  2  0  2  0  2  2  0  2  2  2  0  0  0  2

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+88x^76+16x^78+204x^80+52x^82+335x^84+450x^86+970x^88+832x^90+602x^92+156x^94+168x^96+28x^98+95x^100+2x^102+56x^104+31x^108+9x^112+1x^140

The gray image is a code over GF(2) with n=356, k=12 and d=152.
This code was found by Heurico 1.16 in 3.03 seconds.